I have NO experience with Abstract Algebra whatsoever, but for some reason i felt like taking a stab at this.

According to Wikipedia, an Abelian group is a group (G,*) such that a*b = b*a for all a,b in G.

now we are told that , for any in G

this means that we can write, or alternatively, . Which is the exact definition of an Abelian Group.

don't take my word for it though, wait until the experts get here