# Horizontal Line in Array

You're missing the vertical line | in the column specification and a \multicolumn{1}{r} for the element in the top left corner:

\documentclass{article}

\begin{document}

$\left( \begin{array}{ r | *{3}{r} } \multicolumn{1}{r}{2} & 2 & -1 & 3 \\ \cline{2-4} 0 & 1 & 3 & 4 \\ 0 & 1 & 3 & 4 \\ 0 & 3 & 9 & 6 \\ 0 & 1 & 3 & -2 \end{array} \right)$

\end{document}

For a more evenly distributed spacing around the last three columns, consider using \phantom{-}2 in the first row:

\documentclass{article}

\begin{document}

$\left( \begin{array}{ r | *{3}{r} } \multicolumn{1}{r}{2} & \phantom{-}2 & -1 & 3 \\ \cline{2-4} 0 & 1 & 3 & 4 \\ 0 & 1 & 3 & 4 \\ 0 & 3 & 9 & 6 \\ 0 & 1 & 3 & -2 \end{array} \right)$

\end{document}

With nicematrix. The environments of nicematrix create PGF/Tikz nodes under the rows, columns and cells and the array and it's possible to use them to draw whatever you want with Tikz.

\documentclass{article}
\usepackage{nicematrix}
\usepackage{tikz}

\begin{document}

$\begin{pNiceMatrix}[r,right-margin,columns-width=auto] 2 & 2 & -1 & 3 \\ 0 & 1 & 3 & 4 \\ 0 & 1 & 3 & 4 \\ 0 & 3 & 9 & 6 \\ 0 & 1 & 3 & -2 \CodeAfter \tikz \draw ([xshift=4pt]row-6-|col-2) |- (row-2-|col-5) ; \end{pNiceMatrix}$

\end{document}