Which equation demonstrates the inverse property of multiplication?

• A. A × (1/A) = 1
• B. A × A = A
• C. A × 0 = 0
• D. A × (A + B) = A × A + A × B

Answer: (A)

The inverse property of multiplication is shown when a nonzero number is multiplied by its reciprocal and the product is 1. For any nonzero value a, a × (1/a) = 1. This works because the reciprocal 1/a is defined only when a is not zero, so you’re finding the partner that brings the product to one.

Why this is the best example here: it directly demonstrates that multiplying a number by the number that undoes it yields unity, which is exactly what the inverse property describes.

Multiplying a number by itself, a × a, does not generally give 1, so it isn’t illustrating an inverse relationship. Multiplying by zero always results in zero, which is a separate zero-property of multiplication. The distributive property, shown by a × (a + b) = a × a + a × b, involves distributing multiplication over addition rather than finding a multiplicative inverse.