%% 
%%  An UIT Edition example
%% 
%%  Example 04-02-2 on page 35.
%% 
%%  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}
\makeatletter
\newif\if@borderstar
\def\bordermatrix{\@ifnextchar*{%
\@borderstartrue\@bordermatrix@i}{\@borderstarfalse\@bordermatrix@i*}%
}
\def\@bordermatrix@i*{\@ifnextchar[{\@bordermatrix@ii}{\@bordermatrix@ii[()]}}
\def\@bordermatrix@ii[#1]#2{%
\begingroup
\m@th\@tempdima8.75\p@\setbox\z@\vbox{%
\def\cr{\crcr\noalign{\kern 2\p@\global\let\cr\endline }}%
\ialign {$##$\hfil\kern 2\p@\kern\@tempdima & \thinspace %
\hfil $##$\hfil && \quad\hfil $##$\hfil\crcr\omit\strut %
\hfil\crcr\noalign{\kern -\baselineskip}#2\crcr\omit %
\strut\cr}}%
\setbox\tw@\vbox{\unvcopy\z@\global\setbox\@ne\lastbox}%
\setbox\tw@\hbox{\unhbox\@ne\unskip\global\setbox\@ne\lastbox}%
\setbox\tw@\hbox{%
$\kern\wd\@ne\kern -\@tempdima\left\@firstoftwo#1%
\if@borderstar\kern2pt\else\kern -\wd\@ne\fi%
\global\setbox\@ne\vbox{\box\@ne\if@borderstar\else\kern 2\p@\fi}%
\vcenter{\if@borderstar\else\kern -\ht\@ne\fi%
\unvbox\z@\kern-\if@borderstar2\fi\baselineskip}%
\if@borderstar\kern-2\@tempdima\kern2\p@\else\,\fi\right\@secondoftwo#1 $%
}\null \;\vbox{\kern\ht\@ne\box\tw@}%
\endgroup}
\makeatother
\AtBeginDocument{\setlength\parindent{0pt}}
\StartShownPreambleCommands

\StopShownPreambleCommands
\begin{document}
$\bordermatrix{ &  1 &  2 \cr 1 & x1 & x2 \cr 2 & x3 & x4 \cr 3 & x5 & x6 }$
$\bordermatrix[{[]}]{ &  1 &  2 \cr 1 & x1 & x2 \cr 2 & x3 & x4 \cr 3 & x5 & x6 }$
$\bordermatrix[\{\}]{ &  1 &  2 \cr 1 & x1 & x2 \cr 2 & x3 & x4 \cr 3 & x5 & x6 }$
$\bordermatrix*{ x1 & x2 & 1 \cr x3 & x4 & 2 \cr x5 & x6 & 3 \cr 1 &  2 }$

$\bordermatrix*[{[]}]{ x1 & x2 & 1 \cr x3 & x4 & 2 \cr x5 & x6 & 3 \cr 1 &  2 }$
$\bordermatrix*[\{\}]{ x1 & x2 & 1 \cr x3 & x4 & 2 \cr x5 & x6 & 3 \cr 1 &  2 }$
\end{document}