An efficient way to calculate the inverse of a square matrix A of order n is as follows: (a) Place the nth-order unit matrix I at the right of the matrix A to form an n-row, 2n-column array, which we denote by (AI). (b) Perform Gauss-Jordan elimination on the rows of (AI) so as to reduce the A portion of (AI) to the unit matrix. At the end of this process, the array will have the form (IB). The matrix B is A-1. (If A-1 does not exist, it will be impossible to reduce the A portion of the array to I.) Use this procedure to find the inverse of the matrix in Prob. 8.50.