Construct the augmented matrix for the matrix of interest with identity matrix , then produce a reduced echelon form (REF).

CASE I: The REF is given in the form with identity matrix in the left side. Then , and the matrix in the right side gives the inverse .

CASE II: Otherwise, the size of pivot positions in the leftmost columns must be less than . For example,

EXAMPLE 4. Find the inverse of the matrix , if it exists.

EXAMPLE 5 Find the inverse of the matrix , if it exists.

EXAMPLE 6 Decide whether is invertible or not.

Department of Mathematics