Could someone walk me through the proofs for the following:

Let $\displaystyle <G, \circ>$ be a group with identity $\displaystyle e$. Then

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

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

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