Could someone walk me through the proofs for the following:

Let <G, \circ> 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'.