In this particular case, a simple fix is:
\documentclass{article}
\usepackage{amsmath,stackengine}
\stackMath
\begin{document}
\[
A =
\begin{matrix}
1\\2\\3\\4\\5\\6\\7\\8\\9\\10
\end{matrix}
\stackon[1pt]{\begin{pmatrix}
0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\
0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
\end{pmatrix}
}{
\begin{matrix}
~1&2&3&4&5&6&7&8&9&10
\end{matrix}
}
\]
\end{document}

If you indeed wanted the labels in bold,
\documentclass{article}
\usepackage{amsmath,tabstackengine}
\TABstackTextstyle{\bfseries}
\setstacktabbedgap{9.2pt}
\begin{document}
\[
A =
\tabbedCenterstack[r]{1\\2\\3\\4\\5\\6\\7\\8\\9\\10}
\stackon[1pt]{$\begin{pmatrix}
0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\
0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
\end{pmatrix}$%
}{%
\;\;\tabbedCenterstack{1&2&3&4&5&6&7&8&9&10}%
}
\]
\end{document}
