You know that elements in a group are always invertible, so what happens when you multiply the identity by .
As for texts in groups, Rotman's An Introduction to the theory of groups is very good in my opinion.
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
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 or is it ?
Then what?
we know
and
Does this help?
What is the best and most comprehensive text on groups that starts at the absolute beginning?