Create a block matrix with four quadrants

Question

I want to create a block matrix of this form:

But Block A should be a diagonal matrix with 1 on the diagonal, the other blocks should be B, C and D like in the picture. But the size of each block should be equal.

Answer 1

If you put A in a box you can use its size in the other three quadrants:

\documentclass{article}
\usepackage{amsmath}
\begin{document} 
\[
\sbox0{$\begin{matrix}1&2&3\\0&1&1\\0&0&1\end{matrix}$}
%
C=\left[
\begin{array}{c|c}
\usebox{0}&\makebox[\wd0]{\large $B$}\\
\hline
  \vphantom{\usebox{0}}\makebox[\wd0]{\large $C$}&\makebox[\wd0]{\large $D$}
\end{array}
\right]
\]
\end{document}