Failure to produce nested matrix with shortcut macro

Question

I use a \arr macro as a shortcut for bmatrix environments. In addition, I use a hacked version of bmatrix (see: What's the best way make an “augmented” coefficient matrix?) so that it's easier to typeset augmented matrices.

In theory, \arr{SOMETHING} should be equivalent to \begin{bmatrix}SOMETHING\end{bmatrix}, and most of the time it is. For instance,

\[
\arr   {  2 &  5 }
\arr   {  1 \\ 2 },
\arr   {  1 &  3 }
\arr   {  1 \\ 2 }
\]

produces

However, when I put the lines above inside another \arr, in order to obtain a nested matrix, it blows up

\[
\arr{
\arr   {  2 &  5 }
\arr   {  1 \\ 2 } \\
\arr   {  1 &  3 }
\arr   {  1 \\ 2 }
}
\]

with an error that says "incomplete \ifdim", whereas

\begin{bmatrix}
  \begin{bmatrix}
    2 & 5
  \end{bmatrix}
  \begin{bmatrix}
    1 \\ 2
  \end{bmatrix}
  \\
  \begin{bmatrix}
    1 & 3
  \end{bmatrix}
  \begin{bmatrix}
    1 \\ 2
  \end{bmatrix}
\end{bmatrix}

works

Why?

Below follows the code

\documentclass[a4paper,11pt]{article}
\usepackage{amsmath}
\usepackage{marvosym}
\usepackage{wasysym}
\usepackage{amssymb}

\makeatletter

% https://tex.stackexchange.com/questions/2233/
\renewcommand*\env@matrix[1][*\c@MaxMatrixCols r]{%
  \hskip -\arraycolsep
  \let\@ifnextchar\new@ifnextchar
  \array{#1}}

\newcommand{\arr}[2][\@empty]{%
  \setbox\@tempboxa\hbox{#1}
  \ifdim\wd\@tempboxa=0pt
  \begin{bmatrix}#2\end{bmatrix}
  \else
  \begin{bmatrix}[#1]#2\end{bmatrix}
  \fi
}

\makeatother


\begin{document}

\[
\arr   {  2 &  5 }
\arr   {  1 \\ 2 },
\arr   {  1 &  3 }
\arr   {  1 \\ 2 }
\]
% \[
% \arr{
% \arr   {  2 &  5 }
% \arr   {  1 \\ 2 } \\
% \arr   {  1 &  3 }
% \arr   {  1 \\ 2 }
% }
% \]
% \[
% \begin{bmatrix}
%   \begin{bmatrix}
%     2 & 5
%   \end{bmatrix}
%   \begin{bmatrix}
%     1 \\ 2
%   \end{bmatrix}
%   \\
%   \begin{bmatrix}
%     1 & 3
%   \end{bmatrix}
%   \begin{bmatrix}
%     1 \\ 2
%   \end{bmatrix}
% \end{bmatrix}
% \]
\end{document}

EDIT: unsimplified definition of \arr follows:

\newcommand{\arr}{\@ifstar\arr@star\arr@nostar}
\newcommand{\arr@nostar}[2][\@empty]{%
  \setbox\@tempboxa\hbox{#1}\ifdim\wd\@tempboxa=0pt
  \begin{bmatrix}#2\end{bmatrix}
  \else \begin{bmatrix}[#1]#2\end{bmatrix} \fi
}
\newcommand{\arr@star}[2][\@empty]{%
  \setbox\@tempboxa\hbox{#1}\ifdim\wd\@tempboxa=0pt
  \begin{matrix}#2\end{matrix}
  \else \begin{matrix}[#1]#2\end{matrix} \fi
}

Answer 1

\setbox is a rather error prone way to test if an argument is empty, but here I don't think you need the test at all:

\documentclass[a4paper,11pt]{article}
\usepackage{amsmath}
\usepackage{marvosym}
\usepackage{wasysym}
\usepackage{amssymb}

\makeatletter

% http://tex.stackexchange.com/questions/2233/
\renewcommand*\env@matrix[1][*\c@MaxMatrixCols r]{%
  \hskip -\arraycolsep
  \let\@ifnextchar\new@ifnextchar
  \array{#1}}


\newcommand{\arr}{\@ifstar\arr@star\arr@nostar}

\newcommand{\arr@star}[2][*\c@MaxMatrixCols r]{%
  \begin{matrix}[#1]#2\end{matrix}%
}

\newcommand{\arr@nostar}[2][*\c@MaxMatrixCols r]{%
  \begin{bmatrix}[#1]#2\end{bmatrix}%
}



\makeatother


\begin{document}

\[
\arr   {  2 &  5 }
\arr   {  1 \\ 2 },
\arr   {  1 &  3 }
\arr   {  1 \\ 2 }
\]
 \[
 \arr{
 \arr   {  2 &  5 }
 \arr   {  1 \\ 2 } \\
 \arr   {  1 &  3 }
 \arr   {  1 \\ 2 }
 }
 \]
% \[
% \begin{bmatrix}
%   \begin{bmatrix}
%     2 & 5
%   \end{bmatrix}
%   \begin{bmatrix}
%     1 \\ 2
%   \end{bmatrix}
%   \\
%   \begin{bmatrix}
%     1 & 3
%   \end{bmatrix}
%   \begin{bmatrix}
%     1 \\ 2
%   \end{bmatrix}
% \end{bmatrix}
% \]
\end{document}