I have to show that the following group $$ (G, * , e) $$ with its operation $*$, which is defined through $ g*g = e$ for every $g \in G $ is an abelian group.
In order to do that one have only to show that the group is commutative.
How can one prove it whereas the operation is defined always between an Element and itself?
I reckon it is not so simple as it seems
Thanks in advance for your help :)