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\documentclass[a4paper,fleqn,11pt]{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[ngerman]{babel}
\usepackage{amsmath}
\usepackage{amssymb}

\usepackage{libertine}
\usepackage[libertine]{newtxmath}

\usepackage{graphicx}
\usepackage{gauss}

\newcommand\swaparrow{%
\text{\reflectbox{$\begin{gmatrix}
\mbox{}\\
\mbox{}
\rowops
\swap{0}{1}
\end{gmatrix}$}}\hspace{-4pt}}

\newcommand{\adddown}[1]{%
\text{\reflectbox{$\begin{gmatrix}
\mbox{}\\
\mbox{}
\rowops
\add[\text{\reflectbox{$#1$}}]{0}{1}
\end{gmatrix}$}}\hspace{-4pt}}

\begin{document}

\[\swaparrow\left(\,\begin{matrix}
2 & 2\\
1 & 2
\end{matrix}\,\right.\left|\;\begin{matrix}4\\ 3\end{matrix}\,\right)
\longrightarrow
\adddown{-2}
\left(\,\begin{matrix}
1 & 2\\
2 & 2
\end{matrix}\,\right.\left|\;\begin{matrix}3\\ 4\end{matrix}\,\right)
\longrightarrow
\begin{matrix}
\\
\text{\footnotesize $-\tfrac{1}{2}\,{\cdot}$}
\end{matrix}
\left(\,\begin{matrix}
1 & 2\\
0 & -2
\end{matrix}\,\right.\left|\;\begin{matrix}3\\ -2\end{matrix}\,\right)
\]

\end{document}