alleryDoes the rational number 0 have a multiplicative inverse?
AYes, it is 0 itself
BYes, it is 1
CNo, because 1/0 is undefined
DYes, but only when multiplied by another zero
Answer & Solution
Correct answer: C. No, because 1/0 is undefined
For any non-zero rational a, the multiplicative inverse is 1/a.
But 1/0 is not defined (division by zero is forbidden), so 0 has no multiplicative inverse.
**Equivalently:** there is no rational number x such that 0 × x = 1.
Keep practising Unit 1A3: Function Composition and Inverses
Browse all Unit 1A3: Function Composition and Inverses questions for AP Calculus AB, or explore more Mathematics topics.
Related questions
How many PERFECT SQUARES lie strictly between 100 and 200?Using prime factorisation, √324 equals:The sum 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 equals:Which of the following is a perfect square?Which of the following is NOT a perfect square?Three rational numbers a, b, c are given. Which of the following is ALWAYS true?For which rational number a is the statement 'a is its own additive inverse' TRUE?Using distributivity, the value of (7/5) × (−3/12) + (7/5) × (5/12) is: