I need to come up with a geometric example of a group. I've been given an example, the set of all symmetries of an equilateral triangle. But I then have to show that the axioms are satisfied and I dont really understand how they are.
I know the axioms are the following, given a set X and an operation *: (X x X) --> X then (X,*) is a group if:
(1) there exists a neutral element e such that x*e=e*x=x for all x in X
(2) the operation is associative
(3) every element x in X has an inverse y such that x*y=y*x=e