I have a homework question and I don't know how to approach this exercise.
The exercise is the following:
Let's suppose $G$ is a set with binary function * defined for its members, which is:
- there's $e\in G$, so that $a\star e=a$ where $a\in G$;
- for each $a\in G$, there's a $b\in G$ so that $a\star b=e$.
Prove that $G$ is a group.
I have no Idea how approach this exercise.
pay attention that 3,4 are Noncommutative.