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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