Question

Algorithm to find inverse of a matrix n*n

Answer 1

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

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

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

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

Finally, to get the adjoint, just take the previous
matrix's transpose:


[-12 76 -60 -36]
[-56 208 -82 -58]
[4 4 -2 -10]
[4 4 20 12]

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