# Back to Basics: What is a Multiplicative Inverse?

What is a multiplicative inverse? If that's the question bugging you, this write-up has all the answers. The examples and the definition presented here, will clear out this math concept for you.

Omkar Phatak

Last Updated: Jan 12, 2019

Definition

*When you multiply any number by another number and the resultant product of multiplication is 1, the two numbers are said to be multiplicative inverses of each other*. Inverse of a variable x is often denoted as '1/x' or 'x

^{-1}'. In equation form, it can be defined as follows:

*a x a*

^{-1}= 1^{-1}' are multiplicative inverses of each other, as their product yields 1, which is also known as '

*multiplicative identity*'. This property is applicable to all numbers, and they are almost always distinct numbers, except in a few cases.

Exceptions and Special Cases

The only number which does not have a multiplicative inverse is 0. That is because (1/0) is an undefined quantity, which is also known as a singularity. As you can see, zero is a very special number and has some peculiar properties. Also 1 is the only number, which is its own inverse, for obvious reasons.

Examples

- The inverse of ½ is 2 as (½) x 2 = 1.
- The inverse of 6/5 is 5/6 as (6/5) x (5/6) = 1.
- The inverse of 1 is 1, as 1 x 1 = 1.
- The inverse of 0.25 is 4, as 0.25 x 4 = 1
- The inverse of 1000 is 0.001 as 0.001 x 1000 = 1.