I'm new to groups and trying to answer the following question.

Let G be any group. Show that the identity e is the unique solution of the equation $\displaystyle x^2=x$

So how do I proceed?

A group, as far as my primitive understanding goes, is a set governed by a binary operation, producing local inbred offspring; then we have the given axioms: closure, associativity, identity and invertibility.

So we assume G is a group with a binary operation $\displaystyle x*x=x^2$or is it $\displaystyle x^2-1 $?

Then what?

we know $\displaystyle x*e=xe-1=x$

and $\displaystyle e*e=e^2-1=e$

Does this help?

What is the best and most comprehensive text on groups that starts at the absolute beginning?