Woodbury-Sherman-Morrison formula to compute Matrix Inverse is applicable to a wide, but still restricted type of Invertible matrices. A more general , direct method is the Gauss Jordan method.

Dear Majeed,

Just google "Matrix Inverse" to show thousands of articles about the matrix inverse. It is direct and elementary.

An nxn matrix A is invertible if and only if it has non zero determinant.

Its inverse matrix has the same size with entries can be determined by several methods as A-1 =(adjoint A)/det(A) where the entries of the adjoint matrix are the transpose of the cofactor matrix.

Another approach to use the augmented matrix (A..I) and then transform into reduced row echelon form (I.. A-1), many methods are available.

For large n, and ill matrices there are special methods to follow.

See:

(1) mathworld.wolfram.com/MatrixInverse.html

(2) www.ti3.tuhh.de/paper/rump/Ru08a.pdf

Best regards

Fisrt of all, the matrix must be invetible, i.e. the matrix must not be singular.

The most general direct methods are the Gauss-Jordan method and you can also use the inverse of the determinant times the adjunct.

Dear all,

Thanks for the answers, please I know the Gauss and Gauss-Jordan but I thought there is simpler method and general without need to elementry operations to get the inverse,.

Thanks