**By matrix multiplication we can write:**

(A + B)^{2} = (A+B)(A+B) = A^{2} + AB + BA + B^{2}

**We know that matrix multiplication is not commutative but it is given that : AB = BA**

∴ (A + B)^{2} = A^{2} + AB + AB + B^{2}

**⇒ (A + B)**^{2} = A^{2} + 2AB + B^{2} …proved