Question

Calculate the products A B and B A to verify that B is the inverse of A A= [ 4 1] [ 7 2] B= [2 -1] [-7 4]

Answer 1

To verify the inverse of matrix A, calculate the products AB and BA and check if they both equal the identity matrix.

Step-by-step explanation:

To verify that B is the inverse of A, we need to calculate the products AB and BA.

AB = A * B = [4 * 2 + 1 * (-7), 4 * (-1) + 1 * 4; 7 * 2 + 2 * (-7), 7 * (-1) + 2 * 4] = [2, 0; 0, 2]

BA = B * A = [2 * 4 + (-1) * 7, 2 * 1 + (-1) * 2; (-7) * 4 + 4 * 7, (-7) * 1 + 4 * 2] = [1, 0; 0, 1]

Since AB = BA = I, where I is the identity matrix, we can conclude that B is the inverse of A.