Let $(G, \circ )$ be a group where $a\circ a =e, \ \forall a\in G $. Show that $(G, \circ )$ is abelian.
Let X be a set with an associative binary operation ◦ with identity e. Suppose every element of X satisﬁes x ◦ x = e. Prove that ◦ is commutative.