Which equation demonstrates the multiplicative identity property of one?

Which equation demonstrates the multiplicative identity property of one?

• A. A × 1 = A
• B. A × 1 = 0
• C. A × 0 = A
• D. A × A = 1

Answer: (A)

Multiplicative identity means there is a number that leaves any number unchanged when you multiply by it. For multiplication, that number is 1. So for any value A, A × 1 = A shows this property perfectly—the 1 acts as a neutral element, not changing the value of A. Why the other forms don’t show this identity: multiplying by zero always gives zero, which isn’t the original number unless the number itself is zero, so it’s the zero property, not the identity. And A × A = 1 only holds for certain values of A (like 1 or -1 in the real numbers), not for every A, so it isn’t the universal identity.

Multiplicative identity means there is a number that leaves any number unchanged when you multiply by it. For multiplication, that number is 1. So for any value A, A × 1 = A shows this property perfectly—the 1 acts as a neutral element, not changing the value of A.

Why the other forms don’t show this identity: multiplying by zero always gives zero, which isn’t the original number unless the number itself is zero, so it’s the zero property, not the identity. And A × A = 1 only holds for certain values of A (like 1 or -1 in the real numbers), not for every A, so it isn’t the universal identity.