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

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

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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

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