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 iff $$\left|{x}\right| = 2$$.

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

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