Q. 695.0( 2 Votes )

# If A and B

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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