# Definition:Involution (Mapping)/Definition 3

## Definition

Let $A$ be a set.

Let $f: A \to A$ be a mapping on $A$.

Then $f$ is an involution if and only if $f$ is both a bijection and a symmetric relation.

That is, if and only if $f$ is a bijection such that $f = f^{-1}$.

## Also known as

An involution is also known as an involutive mapping or an involutive function.

An involutive mapping can also be found described as self-inverse.

## Also see

• Results about involutions can be found here.