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Q.

If A and B are two square matrices of the same size, then (A+B)2=A2+2AB+B2can hold if and only  if

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a

AB = BA

b

AB + BA = O

c

|AB| ≠ 0

d

|AB| = 0

answer is A.

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Detailed Solution

(A+B)2=(A+B)(A+B)=A2+BA+AB+B2∴(A+B)2=A2+2AB+B2  if and only if  AB = BA
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If A and B are two square matrices of the same size, then (A+B)2=A2+2AB+B2can hold if and only  if