%% 
%%  An UIT Edition example
%% 
%%  Example 10-10-5 on page 224.
%% 
%%  Copyright (C) 2010 Herbert Voss
%% 
%%  It may be distributed and/or modified under the conditions
%%  of the LaTeX Project Public License, either version 1.3
%%  of this license or (at your option) any later version.
%% 
%%  See http://www.latex-project.org/lppl.txt for details.
%% 
%% 
%% ==== 
% Show page(s) 1
%% 
\documentclass[]{exaarticle}
\pagestyle{empty}
\setlength\textwidth{375.57637pt}
\AtBeginDocument{\setlength\parindent{0pt}}
\StartShownPreambleCommands
\usepackage{amsmath,amssymb}
\makeatletter
\def\underbraceMatrix{\@ifnextchar[{\underbraceM@i}{\underbraceM@i[4pt]}}
\def\underbraceM@i[#1]#2{\underbraceM@ii{#2}{#1}}%
\def\underbraceM@ii#1#2{\mathop{\vtop{\m@th\ialign{##\crcr
   $\hfil\displaystyle{#1}\hfil$\crcr\noalign{\kern3\p@\nointerlineskip}%
   \kern#2\upbracefill\kern#2\crcr\noalign{\kern3\p@}}}}\limits}
\makeatother
\StopShownPreambleCommands
\begin{document}
\[ \underbrace{%
   \left(\begin{array}{cc}
    A_{\cal E E} & A_{\cal E I}\\ A_{\cal I E} & A_{\cal I I}
   \end{array}\right)}_{\textstyle=A}
   \underbraceMatrix{%
   \left(\begin{array}{cc}
    A_{\cal E E} & A_{\cal E I}\\ A_{\cal I E} & A_{\cal I I}
 \end{array}\right)}_{\textstyle=A}
 \underbraceMatrix[1em]{%
 \left(\begin{array}{cc}
    A_{\cal E E} & A_{\cal E I}\\ A_{\cal I E} & A_{\cal I I}
 \end{array}\right)}_{\textstyle=A} \]
\end{document}