Which statement demonstrates the multiplicative inverse concept for a nonzero number?

• A. 1 / a is the multiplicative inverse of a
• B. a is the multiplicative inverse of 1
• C. a is the multiplicative inverse of 0
• D. a^2 is the multiplicative inverse of a

Answer: (A)

The multiplicative inverse of a nonzero number is the number you multiply by to get 1. For any nonzero a, multiplying a by 1/a gives 1, so 1/a is the multiplicative inverse of a. This is why this statement is the best description of the inverse concept.

Think about why the other ideas don’t fit in general: if a were the inverse of 1, then a·1 would have to equal 1, which would force a to be 1 in every case—not true for every nonzero a. The inverse of 0 can’t exist because no number multiplied by 0 can yield 1. And if a^2 were the inverse of a, you’d need a^2·a = 1, meaning a^3 = 1, which only happens for specific values of a, not for all nonzero a.