Let $\displaystyle G$ and $\displaystyle H$ be groups and let [tex] G^\star [tex] be the subset of $\displaystyle G X H $ consisting of all $\displaystyle (a, e) $ with $\displaystyle a \in G $

Show the following:

1. $\displaystyle G^\star \cong G $

2. $\displaystyle G^\star $ is a normal subgroup of $\displaystyle G X H $

3. $\displaystyle \frac{(G X H)}{G^\star} \cong H $

I showed the first two just fine, but I'm having slight trouble with number 3. I had shown that it's a homomorphism, but the surjective part I'm stuck on. Could anyone guide me through this?