programming python

Liền kề ma trận python

On Thu, Dec 9, 2010 at 10:03 PM, Rob Beezer wrote:
> Có bất kỳ sự phản đối nào đối với việc phản đối hiện tại. chức năng liên kết []
> [trả về một ma trận các đồng sáng lập] và đổi tên nó thành
> "phân xử"?
> phản đối. Điều đó sẽ bắt đầu quá trình giải phóng "liên kết" cho
> cái gì khác [lý tưởng là chuyển vị liên hợp]

Tôi đã không thể trả lời về vấn đề này trước đây và hôm nay sau khi nhận được
bình luận về vé #10501 Tôi đã bình luận ngay tại đó, đó có thể là một
hơi thiếu lịch sự vì đã hết thời gian và tôi đã không đăng bài đó
bình luận cho chủ đề này [nếu vậy tôi xin lỗi]

Dù sao, đây là một bản sao của bài viết của tôi, trong trường hợp nó hữu ích

Tôi đã nêu một số phản đối, nhưng tôi sẽ nhắc lại

Về việc không dùng "adjoint" có nghĩa là "ma trận của các đồng sáng lập"
1. đó là thuật ngữ tiêu chuẩn và đã có ý nghĩa này trong hiền triết từ lâu
2. "adjugate" là thuật ngữ mới hơn và [IMO] ít tiêu chuẩn hơn - trong
đặc biệt nó không có bản dịch rõ ràng

Khi sử dụng "adjoin" có nghĩa là "chuyển vị liên hợp"
3. "chuyển vị liên hợp" rất dễ nói, và đó thực sự là ý nghĩa của nó
4. "toán tử phụ" cho một ma trận có vẻ không được xác định rõ ràng, bởi vì một
ma trận không phải là toán tử mà chỉ là biểu diễn của toán tử trong
một số cơ sở

Hơn nữa, nếu có hai cách sử dụng xung đột của tên "adjoint", tôi
sẽ thấy hợp lý hơn nếu giữ cách sử dụng đã có
truyền thống trong Sage

Việc sử dụng "liên kết" là phổ biến liên quan đến các dạng bậc hai
afaict [và, như John Cremona đã chỉ ra, là nơi thuật ngữ này bắt nguồn
với Gauss ở dạng bậc hai bậc ba]

Tôi cũng đã chỉ ra một tham chiếu đến Bourbaki mà tôi đã đăng
bên trên. Tôi vẫn chưa tìm thấy tài liệu tham khảo cho "adjugate" mà
thỏa mãn tôi [ý tôi là, nó bắt nguồn từ đâu?] hoặc một tài liệu tham khảo tốt
để biết cách sử dụng "liên kết của ma trận" theo nghĩa "chuyển vị liên hợp"
liên quan đến các toán tử liên kết mà cuối cùng không gây ra một số đau đớn
khi sử dụng nó trong thế giới thực, nơi không phải tất cả các cơ sở đều trực giao
[thậm chí không phải mọi không gian vectơ đều có tích bên trong]

OTOH, tôi chắc chắn đánh giá cao chuyển vị và chuyển vị liên hợp đó
được sử dụng khá nhiều, và do đó tôi nghĩ rằng nó thực sự xứng đáng với tất cả
các phím tắt được đề xuất [T, H, sao, v.v.]

gonzalo

Ma trận liên hợp [hoặc Adjugate] của một ma trận là ma trận thu được bằng cách chuyển vị ma trận cofactor của một ma trận vuông đã cho được gọi là ma trận Adjoint hoặc Adjugate của nó. Adjoint của bất kỳ ma trận vuông 'A' [giả sử] được biểu diễn dưới dạng Adj[A].

Thí dụ.

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

thuộc tính quan trọng.

Tích của ma trận vuông A với ma trận kề của nó tạo ra một ma trận đường chéo, trong đó mỗi mục nhập đường chéo bằng định thức của A.
i. e.

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Một ma trận vuông khác 0 'A' cấp n được gọi là khả nghịch nếu tồn tại một ma trận vuông duy nhất 'B' cấp n sao cho,

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

tính từ [AB] = [tính từ B]. [tính từ A]
adj[k A] = kn-1 adj[A]
A-1 = [tính từ A] /. A
[A-1]-1 = A
[AB]-1 = B-1A-1

Làm thế nào để tìm Adjoin?

Chúng tôi làm theo định nghĩa được đưa ra ở trên.

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

5_______0_______7

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

7 #include 7#include 8

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

9using0

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

1 using3

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

9using5 using6

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

7 using9

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

9using5

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

30_______0_______7

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

9using5

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

9using5

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

45_______0_______5

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

00_______2_______05

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

9using5

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

Java

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

45_______2_______46_______2_______47

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

9using5

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

6_______0_______7

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

10_______3_______40

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

6_______0_______7

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

6_______0_______7

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Determinant value of A

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

6_______0_______7

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

// C++ program to find adjoint and inverse of a matrix07

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

5 // C++ program to find adjoint and inverse of a matrix10

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

7 // C++ program to find adjoint and inverse of a matrix14// C++ program to find adjoint and inverse of a matrix15// C++ program to find adjoint and inverse of a matrix16

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

53// C++ program to find adjoint and inverse of a matrix18

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

53// C++ program to find adjoint and inverse of a matrix18// C++ program to find adjoint and inverse of a matrix21// C++ program to find adjoint and inverse of a matrix22

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

88_______1678_______18

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

46// C++ program to find adjoint and inverse of a matrix18

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

46_______1678_______18// C++ program to find adjoint and inverse of a matrix31// C++ program to find adjoint and inverse of a matrix22

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

2// C++ program to find adjoint and inverse of a matrix34// C++ program to find adjoint and inverse of a matrix31// C++ program to find adjoint and inverse of a matrix18

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

88// C++ program to find adjoint and inverse of a matrix18// C++ program to find adjoint and inverse of a matrix15// C++ program to find adjoint and inverse of a matrix18

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

46// C++ program to find adjoint and inverse of a matrix22

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

8// C++ program to find adjoint and inverse of a matrix31// C++ program to find adjoint and inverse of a matrix16

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

88// C++ program to find adjoint and inverse of a matrix16// C++ program to find adjoint and inverse of a matrix49// C++ program to find adjoint and inverse of a matrix18

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

25// C++ program to find adjoint and inverse of a matrix52

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

10_______3_______40

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

88 // C++ program to find adjoint and inverse of a matrix62

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

055// C++ program to find adjoint and inverse of a matrix96

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

057

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

060// C++ program to find adjoint and inverse of a matrix96// C++ program to find adjoint and inverse of a matrix96

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

46#include 59

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

066

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

9using5

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

072

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

074

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

076// C++ program to find adjoint and inverse of a matrix96

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

078

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

5 #include 04#include 16 #include 17using04

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

086using07

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

5 using09#include 16 #include 17using12

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

094

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

096

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

5 #include 04#include 16 #include 17using04

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

5 #include 08#include 16 #include 17using04

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

5 #include 04#include 16 #include 17using04

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

5 #include 08#include 16 #include 17using04

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

5 #include 04#include 16 #include 17using04

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

5 #include 08#include 16 #include 17using04

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

066

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

145

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

173

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

174// C++ program to find adjoint and inverse of a matrix96

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

176// C++ program to find adjoint and inverse of a matrix15// C++ program to find adjoint and inverse of a matrix18#include 57

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

53// C++ program to find adjoint and inverse of a matrix18

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

53// C++ program to find adjoint and inverse of a matrix18// C++ program to find adjoint and inverse of a matrix21

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

185

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

88// C++ program to find adjoint and inverse of a matrix18

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

46// C++ program to find adjoint and inverse of a matrix18

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

46// C++ program to find adjoint and inverse of a matrix18// C++ program to find adjoint and inverse of a matrix31

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

185#include 57// C++ program to find adjoint and inverse of a matrix31// C++ program to find adjoint and inverse of a matrix18

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

88// C++ program to find adjoint and inverse of a matrix18// C++ program to find adjoint and inverse of a matrix15// C++ program to find adjoint and inverse of a matrix18

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

185// C++ program to find adjoint and inverse of a matrix31// C++ program to find adjoint and inverse of a matrix18#include 57

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

88// C++ program to find adjoint and inverse of a matrix18#include 57// C++ program to find adjoint and inverse of a matrix49// C++ program to find adjoint and inverse of a matrix18

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

212

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

076// C++ program to find adjoint and inverse of a matrix96

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

024_______1680_______07

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

5 using09#include 16 #include 17

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

221

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

222_______1678_______96

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

024_______1680_______07

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

5 using09#include 16 #include 17

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

221

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

5 #include 04#include 16 #include 17using04

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

237_______1678_______96

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

024using07

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

5 using09#include 16 #include 17

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

221

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

247// C++ program to find adjoint and inverse of a matrix96

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

024using07

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

5 using09#include 16 #include 17

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

221

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

066

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

258

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

260

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

066

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

263

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

094

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

266

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

066

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

269

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

272

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

274

______________275

C#

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

276

using

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

278

using

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

280

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

286

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

288

______________289

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

290

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

295

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

297

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

314

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

321

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

7 #include 7#include 8

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Determinant value of A

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

1 using3

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

9using5

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

378

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

381_______3_______40

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

384

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

396

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

400

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

404

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

9using5

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

______________415

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

295

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

422

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

426

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

430

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

9using5

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

437

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

381_______3_______40

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

384

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

499

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

503

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

516_______3_______40

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

384

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Determinant value of A

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

624_______3_______40

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

384

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

628

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

503

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

503

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

503

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Determinant value of A

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

654

Javascript

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

655

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

656

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

657

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

658

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

659

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

660

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

662

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

663

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

666

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

667

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

672

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

677

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

2____56_______3

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

2____56_______5

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

3____56_______7

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

// C++ program to find adjoint and inverse of a matrix5

// C++ program to find adjoint and inverse of a matrix7

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

662

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

717

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

720#include 8

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

667

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Determinant value of A

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

1 using3

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

9using5 using6

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

667

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

733

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

739

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

743_______3_______40

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

735

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

667

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

750

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

667

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

757

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

667

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

667

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

9using5

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

662

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

780

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

426

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

9using5

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

667

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

750

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

733_______3_______40

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

735

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

739

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

743_______3_______40

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

735

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

667

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

817

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

822

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

856

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

  If det[A] != 0
    A-1 = adj[A]/det[A]
  Else
    "Inverse doesn't exist"

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

499

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

863

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

667

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

876

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

885

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

817

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

822

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

817

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

822

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Determinant value of A

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

817

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

A.adj[A] = det[A].I 

I  => Identity matrix of same order as of A.
det[A] => Determinant value of A

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

   A.B = B.A = I
The matrix 'B' is said to be inverse of 'A'.
i.e.,  B = A-1

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

822

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Determinant value of A

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0  Identity matrix of same order as of A.
det[A] => Determinant value of A

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

959

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

961

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

2____0_______963

The Adjoint is :
-12 76 -60 -36 
-56 208 -82 -58 
4 4 -2 -10 
4 4 20 12 

The Inverse is :
-0.136364 0.863636 -0.681818 -0.409091 
-0.636364 2.36364 -0.931818 -0.659091 
0.0454545 0.0454545 -0.0227273 -0.113636 
0.0454545 0.0454545 0.227273 0.136364

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

965

Below example and explanation are taken from here.
5  -2  2  7
1   0  0  3
-3  1  5  0
3  -1 -9  4

For instance, the cofactor of the top left corner '5' is
 + |0   0   3|
...|1   5   0| = 3[1 * -9 - [-1] * 5] = -12.
...|-1 -9   4|
[The minor matrix is formed by deleting the row 
 and column of the given entry.]

As another sample, the cofactor of the top row corner '-2' is
  -|1   0  3|
...|-3  5  0| = - [1 [20 - 0] - 0 + 3 [27 - 15]] = -56.
...|3  -9  4|

Proceeding like this, we obtain the matrix
[-12  -56   4   4]
[76   208   4   4]
[-60  -82  -2  20]
[-36  -58  -10 12]

Finally, to get the adjoint, just take the previous
matrix's transpose:
[-12   76 -60  -36]
[-56  208 -82  -58]
[4     4   -2  -10]
[4     4   20   12]

876

Let A[N][N] be input matrix.

1] Create a matrix adj[N][N] store the adjoint matrix.
2] For every entry A[i][j] in input matrix where 0

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