Question

Let A and B be square matrices of the order 3 × 3. Is (AB)² = A²B²? Give reasons.

Answer 1

As, A and B be square matrices of order 3 × 3.

We have, (AB)² = AB · AB

= A(BA)B

= A(AB)B  ......[If AB = BA]

= AABB

= A²B²

Thus, (AB)² = A²B² is true only if AB = BA.