Completely baffled by this question involving putting matrices in matrices This is homework, so only hints please.

Let $A\in M_{m\times m}(\mathbb{R})$
   , $B\in M_{n\times n}(\mathbb{R})$
   . Suppose there exist orthogonal matrices $P$
    and $Q$
    such that $P^{T}AP$
    and $Q^{T}BQ$
    are upper triangular. Let $C$
    be any $m\times n$ matrix. Then show that there is an orthogonal $R$
   , not depending on $C$
   , such that $$R^{T} \begin{bmatrix}A & C\\
0 & B
\end{bmatrix}R$$
   is upper triangular.

I haven't done any proofs before using matrices containing matrices in them. I have absolutely no idea where to begin. Any ideas?

Take
$$R = \operatorname{diag}(P,Q) = \begin{bmatrix} P \\ & Q \end{bmatrix},$$
and see what happens. Ask if you get stuck.
