Group Element is Self-Inverse iff Order 2

Theorem
Let $\left({S, \circ}\right)$ be a group whose identity is $e$.

An element $x \in \left({S, \circ}\right)$ is self-inverse :
 * $\left\vert{x}\right\vert = 2$

Proof
Let $x \in G: x \ne e$.