Equations including ``tikzpicture`` II

Question

I'm using the same codes as my the answer of my previous question

    \documentclass[12pt,a4paper]{report}
    \usepackage{amsfonts,amsmath,amssymb,amsthm,tikz}
    \usetikzlibrary{calc,matrix}
\begin{document}
\begin{align*}
D &=
\begin{tikzpicture}[
baseline=-\the\dimexpr\fontdimen22\textfont2\relax,
strip/.style = {
    draw=#1,%color
    line width=1em, opacity=0.2,
    shorten <=-2mm,shorten >=-2mm,
                            },
                    ]
\matrix (mtrx)  [matrix of math nodes,
                 column sep=1em,
                 nodes={text height=1ex,text width=2ex},
                 ampersand replacement=\&]
{
|[red]|+  \& |[red]|+  \& |[red]| +
 \\[3.3mm,between origins]
a_1 \& b_1 \& c_1 \& a_1 \& a_2         \\
a_2 \& b_2 \& c_2 \& a_2 \& b_2         \\
a_3 \& b_3 \& c_3 \& a_3 \& b_3         \\
|[blue]|- \& |[blue]|- \& |[blue]|- \\
};
\draw[thick]  (mtrx-4-1.south west) -- (mtrx-2-1.north west);
\draw[thick] (mtrx-4-3.south east)  -- (mtrx-2-3.north east);
\path[draw,strip=blue]
    (mtrx-4-1.center) edge (mtrx-2-3.center)
    (mtrx-4-2.center) edge (mtrx-2-4.center)
    (mtrx-4-3.center)  --  (mtrx-2-5.center);
\path[draw,strip=red]
    (mtrx-2-1.center) edge (mtrx-4-3.center)
    (mtrx-2-2.center) edge (mtrx-4-4.center)
    (mtrx-2-3.center)  --  (mtrx-4-5.center);
\end{tikzpicture} \\
 &= a+b+c\dots
\end{align*}
\end{document}

However I want to replace

If I replace in the codes

\begin{tikzpicture}[
baseline=-\the\dimexpr\fontdimen22\textfont2\relax,
strip/.style = {
    draw=#1,%color
    line width=1em, opacity=0.2,
    shorten <=-2mm,shorten >=-2mm,
                            },
                    ]
\matrix (mtrx)  [matrix of math nodes,
                 column sep=1em,
                 nodes={text height=1ex,text width=2ex},
                 ampersand replacement=\&]
{
|[red]|+  \& |[red]|+  \& |[red]| +
 \\[3.3mm,between origins]
a_1 \& b_1 \& c_1 \& a_1 \& a_2         \\
a_2 \& b_2 \& c_2 \& a_2 \& b_2         \\
a_3 \& b_3 \& c_3 \& a_3 \& b_3         \\
|[blue]|- \& |[blue]|- \& |[blue]|- \\
};
\draw[thick]  (mtrx-4-1.south west) -- (mtrx-2-1.north west);
\draw[thick] (mtrx-4-3.south east)  -- (mtrx-2-3.north east);
\path[draw,strip=blue]
    (mtrx-4-1.center) edge (mtrx-2-3.center)
    (mtrx-4-2.center) edge (mtrx-2-4.center)
    (mtrx-4-3.center)  --  (mtrx-2-5.center);
\path[draw,strip=red]
    (mtrx-2-1.center) edge (mtrx-4-3.center)
    (mtrx-2-2.center) edge (mtrx-4-4.center)
    (mtrx-2-3.center)  --  (mtrx-4-5.center);
\end{tikzpicture}

by

\begin{tikzpicture}[>=stealth]
    \matrix [%
      matrix of math nodes,
      column sep=1em,
      row sep=1em
    ] (sarrus) {%
      a_{11} & a_{12} & a_{13} & a_{11} & a_{12} \\
      a_{21} & a_{22} & a_{23} & a_{21} & a_{22} \\
      a_{31} & a_{32} & a_{33} & a_{31} & a_{32} \\
    };
\path ($(sarrus-1-1.north west)-(0.5em,0)$) edge ($(sarrus-3-1.south west)-(0.5em,0)$)
      ($(sarrus-1-3.north east)+(0.5em,0)$) edge ($(sarrus-3-3.south east)+(0.5em,0)$)
      (sarrus-1-1)                          edge            (sarrus-2-2)
      (sarrus-2-2)                          edge[->]        (sarrus-3-3)
      (sarrus-1-2)                          edge            (sarrus-2-3)
      (sarrus-2-3)                          edge[->]        (sarrus-3-4)
      (sarrus-1-3)                          edge            (sarrus-2-4)
      (sarrus-2-4)                          edge[->]        (sarrus-3-5)
      (sarrus-3-1)                          edge[dashed]    (sarrus-2-2)
      (sarrus-2-2)                          edge[->,dashed] (sarrus-1-3)
      (sarrus-3-2)                          edge[dashed]    (sarrus-2-3)
      (sarrus-2-3)                          edge[->,dashed] (sarrus-1-4)
      (sarrus-3-3)                          edge[dashed]    (sarrus-2-4)
      (sarrus-2-4)                          edge[->,dashed] (sarrus-1-5);

\foreach \c in {1,2,3} {\node[anchor=south] at (sarrus-1-\c.north) {$+$};};
\foreach \c in {1,2,3} {\node[anchor=north] at (sarrus-3-\c.south) {$-$};};

\end{tikzpicture}

It does not work.

Answer 1

For fun, another way using blkarray, an align* environment and pstricks:

\documentclass[svgnames]{article}
\usepackage{blkarray}
\usepackage{amsmath}
\usepackage{pst-node}
\begin{document}
\begin{align}
D & = \begin{blockarray}{ccccc}
  \color{red} + & \color{red} + & \color{red} + \
\begin{block}{|ccc|cc}
\Rnode{a1}{a_{11}} &\Rnode{b1}{ a_{12}} & \Rnode{c1}{a_{13}} & \Rnode{A1}{a_{11}} & \Rnode{B1}{a_{12}} \
\Rnode{a2}{ a_{21}} & \Rnode{b2}{a_{22}} & \Rnode{c2}{a_{23}} & \Rnode{A2}{a_{21} }& a_{22} \
  \Rnode{a3}{a_{31}} & \Rnode{b3}{a_{32}} & \Rnode{c3}{a_{33}} & \Rnode{A3}{a_{31}} & \Rnode{B3}{a_{32}} \
\end{block}
  \color{blue} - & \color{blue} - & \color{blue} -
\end{blockarray} \[-3ex]
& = a_{11} a_{22}a_{33} + a_{12}a_{23}a_{31} + \dots
\psset{linewidth=0.5pt, nodesepA=1pt, nodesepB =1.5pt, arrowinset=0.1}
\foreach \s/\t in {a1/b2,b1/c2,c1/A2} {\ncline{-}{\s}{\t}}
\foreach \s/\t in {b2/c3,c2/A3,A2/B3} {\ncline{->}{\s}{\t}}
\psset{linestyle=dashed, dash=3pt 2pt}
\foreach \s/\t in {a3/b2,b3/c2,c3/A2} {\ncline{-}{\s}{\t}}
\foreach \s/\t in {b2/c1,c2/A1,A2/B1} {\ncline{->}{\s}{\t}}
   %
\end{align}
\end{document}