\listfiles
\documentclass{jarticle}
\usepackage{mathtools}

\begin{document}

\verb|\usepackage{amsmath}|
\begin{align*}
&\begin{matrix}
a_{11} &a_{12} \\
a_{21} &a_{22}+b_{12}
\end{matrix} \\
&\begin{pmatrix}
a_{11} &a_{12} \\
a_{21} &a_{22}+b_{12}
\end{pmatrix}\\
&\begin{bmatrix}
a_{11} &a_{12} \\
a_{21} &a_{22}+b_{12}
\end{bmatrix}\\
&\begin{Bmatrix}
a_{11} &a_{12} \\
a_{21} &a_{22}+b_{12}
\end{Bmatrix}\\
&\begin{vmatrix}
a_{11} &a_{12} \\
a_{21} &a_{22}+b_{12}
\end{vmatrix}\\
&\begin{Vmatrix}
a_{11} &a_{12} \\
a_{21} &a_{22}+b_{12}
\end{Vmatrix}
\end{align*}

\verb|\usepackage{mathtools}|

\verb|\begin{matrix*}[r]|
\begin{align*}
&\begin{matrix*}[r]
a_{11} &a_{12} \\
a_{21} &a_{22}+b_{12}
\end{matrix*} \\
&\begin{pmatrix*}[r]
a_{11} &a_{12} \\
a_{21} &a_{22}+b_{12}
\end{pmatrix*}\\
&\begin{bmatrix*}[r]
a_{11} &a_{12} \\
a_{21} &a_{22}+b_{12}
\end{bmatrix*}\\
&\begin{Bmatrix*}[r]
a_{11} &a_{12} \\
a_{21} &a_{22}+b_{12}
\end{Bmatrix*}\\
&\begin{vmatrix*}[r]
a_{11} &a_{12} \\
a_{21} &a_{22}+b_{12}
\end{vmatrix*}\\
&\begin{Vmatrix*}[r]
a_{11} &a_{12} \\
a_{21} &a_{22}+b_{12}
\end{Vmatrix*}
\end{align*}

\verb|\usepackage{mathtools}|

\verb|\begin{matrix*}[l]|
\begin{align*}
&\begin{matrix*}[l]
a_{11} &a_{12} \\
a_{21} &a_{22}+b_{12}
\end{matrix*} \\
&\begin{pmatrix*}[l]
a_{11} &a_{12} \\
a_{21} &a_{22}+b_{12}
\end{pmatrix*}\\
&\begin{bmatrix*}[l]
a_{11} &a_{12} \\
a_{21} &a_{22}+b_{12}
\end{bmatrix*}\\
&\begin{Bmatrix*}[l]
a_{11} &a_{12} \\
a_{21} &a_{22}+b_{12}
\end{Bmatrix*}\\
&\begin{vmatrix*}[l]
a_{11} &a_{12} \\
a_{21} &a_{22}+b_{12}
\end{vmatrix*}\\
&\begin{Vmatrix*}[l]
a_{11} &a_{12} \\
a_{21} &a_{22}+b_{12}
\end{Vmatrix*}
\end{align*}

\end{document}
