Show that if A and B are square matrices such that AB = BA, then (A + B)2 = A2 + 2AB + B2.
By matrix multiplication we can write:
(A + B)2 = (A+B)(A+B) = A2 + AB + BA + B2
We know that matrix multiplication is not commutative but it is given that : AB = BA
∴ (A + B)2 = A2 + AB + AB + B2
⇒ (A + B)2 = A2 + 2AB + B2 …proved