If $\displaystyle S,T:H\rightarrow H$ are bounded operators, show that $\displaystyle (ST)^*=T^*S^*$.

I'm assuming that $\displaystyle H$ is a Hilbert space, although it doesn't say this in the question. I'm really not sure where to start with this. All I have is that since $\displaystyle S,T$ are bounded there adjoints $\displaystyle S^*$ and $\displaystyle T^*$ exist and that:

$\displaystyle <Tx,y>=<x,T^*y>$ for all $\displaystyle x\in H$,$\displaystyle y\in H$