Group where every element is order 2
Let $(G,\star)$ be a group with identity element $e$ such that $a \star a = e$ for all $a \in G$. Prove that $G$ is abelian.
Ok, what i got is this: we want to prove that a*b=b*a, i.e. if a*a=e , a=a' where a' is the inverse and b*b=e, b=b' where b' is the inverse so a*b=(a*b)'=b'*a'=b*a....