I have a problem, here is the appropriate theorem:

**Theorem:** Let $\displaystyle G$ be a group with operation $\displaystyle *$, and let $\displaystyle H$ be a subset of $\displaystyle G$. Then $\displaystyle H$ is a subgroup of $\displaystyle G$ iff

(a) $\displaystyle H$ is nonempty

(b) if $\displaystyle a \in H$ and $\displaystyle b \in H$, then $\displaystyle a*b \in H$, and

(c) if $\displaystyle a \in H$, then $\displaystyle a^{-1} \in H$

i've used this theorem over and over in studying, but i have trouble proving (b) and (c) in the following problem[B]