Which statement defines the multiplicative inverse (reciprocal) of a nonzero number n?

Which statement defines the multiplicative inverse (reciprocal) of a nonzero number n?

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

Answer: (B)

The multiplicative inverse of a nonzero number n is the number that you multiply n by to get 1. That number is 1/n, so n × (1/n) = 1 for every nonzero n. This works whether n is positive or negative, because the n and 1/n cancel to give 1. The other expressions don’t define the reciprocal: n × n = 1 would only hold when n is 1 or -1; (1/n) × (1/n) = 1 would require 1/n^2 = 1, again only for n = ±1; and n × 0 = 0 uses zero, not the inverse.

The multiplicative inverse of a nonzero number n is the number that you multiply n by to get 1. That number is 1/n, so n × (1/n) = 1 for every nonzero n. This works whether n is positive or negative, because the n and 1/n cancel to give 1. The other expressions don’t define the reciprocal: n × n = 1 would only hold when n is 1 or -1; (1/n) × (1/n) = 1 would require 1/n^2 = 1, again only for n = ±1; and n × 0 = 0 uses zero, not the inverse.