How to prove abelian group I am struggling answering this question for myself:
How can i prove that a Group $G$ is abelian, if $$g\circ g=e \ \forall g \in G $$
A group is abelian if this is true:
$$a\circ b = b\circ a\ \forall a,b \in G$$
But i dont understand how to prove this.
Hope someone can help me out with this!

$a$ and $b$ commute iff $a \circ b = b \circ a$ iff $a \circ b \circ a^{-1} \circ b ^{-1} = e$.
However $a^{-1} = a$ and $b^{-1} = b$ so then $a \circ b \circ a^{-1} \circ b ^{-1} = a \circ b \circ a \circ b = (a \circ b) \circ (a \circ b) = e$ by hypothesis.
