Question

Multiplicative inverse of ‘0’ is
(A) $\dfrac{1}{0}$
(B) 0
(C) Does not exist
(D) $\dfrac{0}{0}$

Answer 1

Hint: In this question we have to find the Multiplicative Inverse of the given number. A multiplicative inverse of a number is defined as the number which is reciprocal of the given number or the multiplication of the number with its multiplicative inverse results in 1. For example, if a given number is $x$ then its multiplicative inverse would be $\dfrac{1}{x}$ and according to the definition of the multiplicative inverse –
$x \times \dfrac{1}{x} = 1$

Complete step-by-step answer:
Given:
The number given is – 0
So according to the definition of the multiplicative inverse, the value of the multiplicative inverse of 0 would be $\dfrac{1}{0}$ but we know that if we divide any number by zero the answer is an undefined value also known as the infinity $\infty $.
Since we do not know the value of the number $\dfrac{1}{0}$, we can say that this value of multiplicative inverse does not exist.
Therefore, the value of the multiplicative inverse of 0 does not exist and the correct answer is –
(C) Does not exist

So, the correct answer is “Option C”.

Note: The other reason that the multiplicative inverse of 0 does not exist is because according to the definition of the multiplicative inverse the product of the number and its multiplicative inverse should be 1 but, in this case, if we multiply 0 with 1 the answer we get is 0 because the product of any number with 0 is always 0. Therefore, the necessary condition required for the number to be a multiplicative inverse is not satisfied and this is the reason that the multiplicative inverse of 0 does not exist.