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:
 * $$\left({I_S}\right)^{-1} = I_S$$

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

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