Question

The multiplicative inverse of _____ and ______ are the numbers themselves.
(a) 1, 0
(b) -1, 1
(c) -1, 0
(d) 0, 1

Answer 1

Hint: Find the multiplicative inverse of 0, 1 and -1. Compare and check the options which fit according to the description of multiplicative inverse.

Complete step-by-step answer:

In mathematics, a multiplicative inverse or reciprocal for a number X denoted as \[\dfrac{1}{X}\] or \[{{X}^{-1}}\] is a number which when multiplied by x yields the multiplicative identity 1.
The multiplicative inverse of a fraction \[\dfrac{a}{b}\] is \[\dfrac{b}{a}\].
Now let us consider some examples of multiplicative inverse.
The multiplicative inverse of 3 is \[\dfrac{1}{3}\].
The multiplicative inverse of 8 is \[\dfrac{1}{8}\].
The multiplicative inverse of \[\dfrac{5}{6}\] is \[\dfrac{6}{5}\].
Similarly for 1, the multiplicative inverse is also 1.
For (-1), the multiplicative inverse is also (-1).
Zero doesn’t have a reciprocal because it is undefined.
Thus looking into each option we can figure out the pair whose multiplicative inverse is the same as that of the number.
In (1, 0) = In multiplicative inverse of 1 is 1 and zero’s reciprocal is undefined.
In (-1, 1) = The multiplicative inverse of both -1 and 1 is the same as -1 and 1.
In (-1, 0) = The inverse of (-1) is (-1) and that of zero’s undefined.
In (0, 1) = The inverse of zero is undefined and the inverse of 1 is 1.
Thus we can say that the pair (-1, 1), both multiplicative inverses, have the same value i.e. the number themselves.
Thus the multiplicative inverse of 1 and (-1) are the numbers themselves.
\[\therefore \] Option (b) is the correct answer.

Note: In the phrase multiplicative inverse, the qualifier multiplicative is often omitted and then tactically understood. Multiplicative inverses can be defined over many mathematical domains as well as number. In case of real numbers, zero does not have a reciprocal as its undefined and because no real number multiplied by zero produces 1.