Question

What is the multiplicative inverse of $\dfrac{0}{1}$?

Answer 1

Hint: Here, in the given question, we need to find the multiplicative inverse of $\dfrac{0}{1}$, which is a fractional number. Multiplicative inverse means the reciprocal of a number. The multiplicative inverse of a number is defined as a number which when multiplied by the original number gives the product as $1$. Let us suppose $''n''$ be any number then its multiplicative inverse can be expressed as $\dfrac{1}{n}$ and ${n^{ - 1}}$. Here, we will find the multiplicative inverse of $\dfrac{0}{1}$ by doing reciprocal of it i.e., replacing numerator value by denominator value and vice-versa.

Complete step-by-step answer:
Here, we are given, a fractional number $\dfrac{0}{1}$
Let us assume that $\dfrac{a}{b}$ is the given number then the multiplicative inverse of the given number can be given by $\dfrac{b}{a}$.
We are asked to find the multiplicative inverse of $\dfrac{0}{1}$
Now, the multiplicative inverse of the fraction can be given as $\dfrac{1}{0}$.
Since, we know that anything divided by zero lasts for infinity and cannot be defined. Hence, the multiplicative inverse of zero does not exist and can be said as undefined.
So, the correct answer is “ undefined”.

Note: Remember that when the number zero is multiplied with any number it gives a resultant value as zero. Don’t get confused between additive inverse and multiplicative inverse, apply them accordingly. The additive inverse can be defined as the number which when added to the original number gives zero as the resultant value whereas the multiplicative inverse is a number which when multiplied by the original number gives the product as $1$.