Answer :

Given that A and B are square matrices of the same order such that AB = BA.


We need to prove that (A + B)2 = A2 + 2AB + B2.


We know (A + B)2 = (A + B)(A + B)


(A + B)2 = A(A + B) + B(A + B)


(A + B)2 = A2 + AB + BA + B2


However, here it is mentioned that AB = BA.


(A + B)2 = A2 + AB + AB + B2


(A + B)2 = A2 + 2AB + B2


Thus, (A + B)2 = A2 + 2AB + B2 when AB = BA.


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