Sami Ashhab

Matrix Inverse

Let M be an n x n matrix, that is,

The inverse of the matrix M is give by the following formula:

where Adj(M) denotes the adjoint of the matrix M and is equal to:

.

denotes the n - 1 x n - 1 submatrix of M obtained by deleting the i th row and j th column of M. det is the determinant. Note that the ( j , i ) element of the inverse matrix is equal to

We have

Example 1:

Exercise: Check that

Example 2: Let us find some of the elements of the adjoint marix of (sI-A).