Question

Let A and B be square matrices of the order 3 × 3. Is (AB)² = A² B²? Give reasons.

 

Answer 1

Yes, (AB)² = A² B² if AB = BA.

If AB = BA, then
 (AB)² = (AB)(AB)
           = A(BA)B      (associative law)
           = A(AB)B
           = A² B²