$A$ is a Hadamard matrix of side $n$, and $H$ is a Hadamard matrix of side $m+n$, where $H=\pmatrix{A& B \\\ C& D}$ for some matrices $B,C,D$. Prove that $m \geq n$.
A Hadamard matrix is a square matrix of side n with entries -1,1 and $HH^t=nI$. I'm assuming I have to use the following facts that I know about Hadamard matrices: The rows and columns are pairwise orthogonal.
Every HM can be normalized ($1$'s in the first row and column)
$n+m$ is 1, 2 or a multiple of $4$
I'm not sure how to prove this...help please.