Showing transitivity of PSPACE?

For the following question:

If B is an element of PSPACE and A is an element of PSPACE-Complete, and A polynomial reduces to B, then B is an element of PSPACE-Complete.

I am trying to prove this, but I don't understand how to get started. Can anyone help please?

If $A$ is PSPACE-Complete, then any $A' \in$ PSPACE can be reduced to $A$ in polynomial time. What can you say about a polynomial time reduction from $A'$ to $B$?