LaTeX: complicated matrix description

matrix.tex

\documentclass[uplatex,dvipdfmx,9pt,a5paper,papersize,fleqn]{jsarticle}
\usepackage{tikz,varwidth}
\usetikzlibrary{matrix,decorations.markings}
\begin{document}

\begin{equation}
  \makebox[0pt][r]{\makebox[\mathindent][l]{1)}}
  P_n(i,j) = \left(\begin{varwidth}[c]{\linewidth}%
    \newcommand{\X}{\phantom{0}}%
    \begin{tikzpicture}[
        mleader/.style={decorate, decoration={markings,
          mark=between positions 0 and 1 step 0.5em with
            { \node {.}; }}},
        tips/.style={font=\footnotesize,align=center}]
      \matrix[matrix of math nodes, nodes in empty cells,
        column sep=0pt, row sep=-2pt] (M) {
        1 &   &   &\X &   &   &   &\X &   &   &   \\
          &\ddots&&   &   &   &   &   &   &   &   \\
          &   & 1 &   &   &   &   &   &   &   &   \\
       \X &   &   & 0 &   &   &   & 1 &   &   &\X \\
          &   &   &   & 1 &   &   &   &   &   &   \\
          &   &   &   &   &\ddots&&   &   &   &   \\
          &   &   &   &   &   & 1 &   &   &   &   \\
       \X &   &   & 1 &   &   &   & 0 &   &   &\X \\
          &   &   &   &   &   &   &   & 1 &   &   \\
          &   &   &   &   &   &   &   &   &\ddots&\\
          &   &   &\X &   &   &   &\X &   &   & 1 \\
      };
      \useasboundingbox (M);
      \draw[mleader](M-4-1.west) node[left=1.2em,tips]{第$i$行→}
          --(M-4-4)--(M-4-8)--(M-4-11.east);
      \draw[mleader](M-8-1.west) node[left=1.2em,tips]{第$j$行→}
          --(M-8-4)--(M-8-8)--(M-8-11.east);
      \draw[mleader](M-1-4.north) node[above=0.2em,tips]{第$i$列\\↓}
          --(M-4-4)--(M-8-4)--(M-11-4.south);
      \draw[mleader](M-1-8.north) node[above=0.2em,tips]{第$j$列\\↓}
          --(M-4-8)--(M-8-8)--(M-11-8.south);
    \end{tikzpicture}%
  \end{varwidth}\right),
  \qquad i \neq j.
\end{equation}
すなわち，$n$次正方行列の，第$i$行と第$j$行とを交換したものが……

\end{document}