Question

Show that if A and B are square matrices such that AB = BA, then (A + B)² = A² + 2AB + B².

Answer 1

Given, A and B are square matrices such that AB = BA.

So, (A + B)² = (A + B) · (A + B)

= A² + AB + BA + B²

= A² + AB + AB + B²  ......[Since, AB = BA]

= A² + 2AB + B²