I saw an old question on how to obtain arrows inside of matrices using arrows. And thanks to Altermundus I was able to hack together the file below:
\documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{matrix}
\usepackage{fullpage,amsmath}
\begin{document}
\begin{align*}
\begin{array}{|rrr|rr}
i & j & k & i & j\\
3 & -2 & 2 & 3 & -2\\
3 & 2 & 1 & 3 & 2
\end{array}
\end{align*}
\begin{figure}[!htbp]
\tikzset{node style ge/.style={circle}}
\centering
\begin{tikzpicture}[baseline=(A.center)]
\tikzset{BarreStyle/.style = {opacity=.4,line width=3 mm,line cap=round,color=#1}}
\tikzset{SignePlus/.style = {above left,,opacity=0.8,circle,fill=#1!50}}
\tikzset{SigneMoins/.style = {above right,,opacity=0.8,circle,fill=#1!50}}
% les matrices
\matrix (A) [matrix of math nodes, nodes = {node style ge},,column sep=0 mm]
{ i & j & k & i & j \\
3 & -2 & 2 & 3 & -2 \\
3 & 2 & 1 & 3 & 2 \\
};
\draw [BarreStyle=red] (A-1-1.north west) node[SignePlus=red] {$+$} to (A-3-3.south east) ;
\draw [BarreStyle=red] (A-1-2.north west) node[SignePlus=red] {$+$} to (A-3-4.south east) ;
\draw [BarreStyle=red] (A-1-3.north west) node[SignePlus=red] {$+$} to (A-3-5.south east) ;
\draw [BarreStyle=blue] (A-1-3.north east) node[SigneMoins=blue] {$-$} to (A-3-1.south west);
\draw [BarreStyle=blue] (A-1-4.north east) node[SigneMoins=blue] {$-$} to (A-3-2.south west);
\draw [BarreStyle=blue] (A-1-5.north east) node[SigneMoins=blue] {$-$} to (A-3-3.south west);
\draw (A-1-1.north west) -- (A-3-1.south west); \draw (A-1-3.north east) -- (A-3-3.south east);
\end{tikzpicture}
\end{figure}
\end{document}

Now I am having a few bunks to iron out, and some help would be much obliged =)
Is there any method to get the absolute signs, eg the brackets
| |around the matrices to be horizontal? Right now they are slanted, due to the different size ofa_{11}and$_{13}.The blue and red lines are also not quite parallel, any fix here?
I was thinking of wrapping this code in a new environment, or something. But I guess that will have to do for a later question. I sort of need to make a few of these, so I would preffer not a quick and dirty fix that works only in this case. My entries are never bigger than 3 digits.

