Answer :

Given that A and B are square matrices of the same order.


We need to check if (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


For the equation (A + B)2 = A2 + 2AB + B2 to hold, we need AB = BA that is the matrices A and B must satisfy the commutative property for multiplication.


However, here it is not mentioned that AB = BA.


Therefore, AB ≠ BA.


Thus, (A + B)2 ≠ A2 + 2AB + B2.


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