I try to solve some exercises from Conway "Functional Analysis", and I have some problems with the following: $P,Q,PQ$ are orthogonal projections.
(1) $PQ$ is orthogonal projection iff $PQ=QP$
I already proved that if $PQ$ is a projection then $PQ=QP$. For the other direction I need to show that $PQ=(PQ)^2$ (because then we know that $PQ$ is idempotent), but I have no idea how to prove it.
For (2) I have no idea.