Question

Let A and B be square matrices of order 3x3. Is (AB)²=A²B²? Give reasons.

Answer 1

Since, A and B are square matrices of the order 3 × 3.
∴ (AB)^2 = AB.AB
= A(BA)B
= A(AB)B [If AB = BA]
= AABB
= A^2 B^2
So, (AB)2 = A^2B^2 is true only if AB = BA.