Matrices with side curly brackets

If you are looking for the following behaviour

Use the following latex code

\usepackage{amsmath}     \begin{equation*}   \mathbf{X} = \begin{array}{c@{\!\!\!}l}   \left[ \begin{array}[c]{ccccc}     1 & 0 & 0 & \cdots & 0 \\     \vdots & \vdots & \vdots && \vdots \\     1 & 0 & 0 & \cdots & 0 \\     \hline     1 & 1 & 0 & \cdots & 0 \\     \vdots & \vdots & \vdots && \vdots \\     1 & 1 & 0 & \cdots & 0 \\     \hline     1 & 0 & 1 & \cdots & 0 \\     \vdots & \vdots & \vdots && \vdots \\     1 & 0 & 1 & \cdots & 0 \\     \hline     \vdots & \vdots & \vdots && \vdots \\     \hline     1 & 0 & 0 & \cdots & 1 \\     \vdots & \vdots & \vdots && \vdots \\     1 & 0 & 0 & \cdots & 1 \\   \end{array}  \right] &  \begin{array}[c]{@{}l@{\,}l}    \left. \begin{array}{c} \vphantom{0}  \\ \vphantom{\vdots}    \\ \vphantom{0} \end{array} \right\} & \text{$n_1$ times} \\ \left. \begin{array}{c} \vphantom{0} \\ \vphantom{\vdots}    \\ \vphantom{0}  \end{array} \right\} & \text{$n_2$ times} \\ \left. \begin{array}{c} \vphantom{0}   \\ \vphantom{\vdots} \\ \vphantom{0} \end{array} \right\} & \text{$n_3$ times} \\   \vphantom{\vdots} & \\ \left. \begin{array}{c} \vphantom{0}   \\ \vphantom{\vdots} \\ \vphantom{0} \end{array} \right\} & \text{$n_l$ times} \end{array} \end{array} \end{equation*}