## Prove Fundamental Group Theorem 2-2

Could someone walk me through the proofs for the following:

Let $$ be a group with identity $e$. Then

1. If a' is a left inverse of a $\in$ G, then a $\circ$ a' = e.

2. If a,b,c $\in$ and a $\circ$ c = b $\circ$ c, then a = b.

3. If a,b $\in$ G and b $\circ$ a = e, then b = a'.