\documentclass{article}
\let\matrix\relax
\makeatletter
\newenvironment{matrix}
{\let\\\cr\null\,\vcenter\bgroup\normalbaselines\m@th\ialign\bgroup
\hfil$##$\hfil&&\quad\hfil$##$\hfil\crcr\mathstrut\crcr\noalign{\kern-\baselineskip}}
{\crcr\mathstrut\crcr\noalign{\kern-\baselineskip}\egroup\egroup\,}
\makeatother
\begin{document}
$\left(\begin{matrix}a & b\\ c & d\end{matrix}\right)$
\end{document}