Inverse of Identity Mapping

Theorem
Let $S$ be a set.

Let $I_S: S \to S$ be the identity mapping on $S$.

Then the inverse of $I_S$ is itself:
 * $\left({I_S}\right)^{-1} = I_S$

Proof
From the nature of the identity mapping, we have:
 * $I_S \circ I_S = I_S$

from which it follows by definition that $I_S$ is the two-sided inverse of itself.