The [[Identity]] [[Function]] for some [[Set]] $X$ is a [[Function]] that when applied is idempotent for any value $x\in X$, denoted as $\op{id}_{X}$.
$\huge
\op{id} : x \mapsto x \\
$
$\huge \op{id_{X}} : X\to X $
The [[Identity|Identity Function]] is [[Bijective]], with the [[Inverse Function]] of $\op{id}$ being $\op{id}$.
$\huge
\op{id}_{X}^{-1} = \op{id_{X}}
$