Let $\langle G,*\rangle$ be an abelian group with identity element $e$. Prove that $H = \{x ∈ G | x ∗ x = e\}$ is a subgroup of $G$
If $G$ is abelian, then the set of all $g \in G$ such that $g = g^{-1}$ is a subgroup of $G$