We first give a consequence of Theorem 2.5.8 and then use it to find the inverse of an invertible matrix.

**Summary:** Let
be an
matrix. Apply the
Gauss-Jordan method to the matrix
Suppose the row reduced echelon form of the matrix
is
If
then
or else
is not invertible.

**Solution:** Consider the matrix
A sequence of steps in the Gauss-Jordan
method are:

- Thus, the inverse of the given matrix is

A K Lal 2007-09-12