Which equation demonstrates the commutative property of multiplication?

Which equation demonstrates the commutative property of multiplication?

• A. A × B = B × A
• B. A × B = A × B
• C. A × (B + C) = A × B + A × C
• D. A × (B - C) = A × B - A × C

Answer: (A)

Multiplication is commutative: swapping the order of the factors doesn’t change the product. The statement A × B = B × A shows this directly, since it says you can swap A and B and still get the same result (for example, 3 × 4 = 4 × 3 = 12). The other equations illustrate different ideas: A × B = A × B is just a true statement that doesn’t demonstrate swapping order; A × (B + C) = A × B + A × C shows the distributive property over addition; and A × (B - C) = A × B - A × C shows distributive property over subtraction.

Multiplication is commutative: swapping the order of the factors doesn’t change the product. The statement A × B = B × A shows this directly, since it says you can swap A and B and still get the same result (for example, 3 × 4 = 4 × 3 = 12).

The other equations illustrate different ideas: A × B = A × B is just a true statement that doesn’t demonstrate swapping order; A × (B + C) = A × B + A × C shows the distributive property over addition; and A × (B - C) = A × B - A × C shows distributive property over subtraction.