Wie setze ich die math-Nodes rechtsbündig in einer TikZ-Matrix?

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\documentclass{article}
\usepackage[ngerman]{babel}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{matrix}
\begin{document}
alignment SOLL: \\
$\left\lgroup\begin{array}{r r r| r}
3   & -3       & 0        & 1 \\ 
-3  & \frac92  & -\frac32 & 3 \\ 
0   & -\frac32 & \frac32  & 2 \\ 
\end{array}\right\rgroup$ \\ \\
alignment IST: \\
\tikzset{mymatrix/.style={
matrix of math nodes,
left delimiter=\lgroup,right delimiter=\rgroup,
inner sep=0pt, column sep=0.5em, %row sep=0.1em,
nodes={inner sep=0.25em,text width=1em,},
column 1/.style={align=right},
column 2/.style={align=right},
column 3/.style={align=right}
}}
\begin{tikzpicture}
\matrix (m) [mymatrix]
{
3   & -3       & 0        & 1 \\ 
-3  & \frac92  & -\frac32 & 3 \\ 
0   & -\frac32 & \frac32  & 2 \\ 
};
\draw[]  (m-1-4.north west) -- (m-3-4.south west);
\node[red] at ([xshift=2em]m-2-4.east) {$\cdot\frac23$};
\node[red] at ([xshift=2em]m-3-4.east) {$\cdot 2$};
\end{tikzpicture}
\end{document}
 
 
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