basic group theory questions

taken from D&F, question 1.1.7:

Let (i.e. ). Show that is an abelian group.

The question asks for verification of the group axioms, although I'm a little confused with showing the existence of inverses. One can say that for an arbitrary , which is the identity. But notice that I said , and that's confusing me. Is ? Is it literally the negative of ? I would presume as much since I actually took that into consideration when I added . But is not part of by construction. So how do I show the existence of inverses?