If A and B are square matrices of the same order, which of the following properties is always valid?

(A) det(A * B) = det(A) * det(B)

(B) A * B = B * A

(C) det(A + B) = det(A) + det(B)

(D) (A + B)^2 = A^2 + 2AB + B^2

Answer Key:

A

### Solution: The determinant of a matrix product is the product of determinants: det(AB) = det(A)det(B). Matrix multiplication is not generally commutative. Correct: A.

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