Matrix Inversion

We are given the matrix , and we need to find its inverse using elementary row transformations. The inverse of a matrix can be found by performing row operations on the augmented matrix , where is the identity matrix. Step 1: Write the augmented matrix: Step 2: Perform row operations to make the diagonal elements equal to 1. We will scale each row by the reciprocal of the corresponding diagonal element. - Row 1: Divide by , Row 2: Divide by , Row 3: Divide by . The result will be: Step 3: The right-hand side is the inverse matrix: