Tikz matrix with array below and braces

Here are two solutions:

1. First one completing your code (full tikz matrix)
2. Second one with both nicematrix and tikz

Code

documentclass{article}
usepackage{tikz}
usetikzlibrary{decorations.pathreplacing,matrix,calc,positioning}
usepackage{nicematrix}
tikzset{ 
    table/.style={
        matrix of math nodes,
        row sep=-pgflinewidth,
        column sep=-pgflinewidth,
        nodes={rectangle,text width=3em,align=center},
        text depth=1.25ex,
        text height=2.5ex,
        nodes in empty cells,
        left delimiter=[,
        right delimiter={]},
        ampersand replacement=&
    }
}

begin{document}
    [
    A=
    begin{tikzpicture}[baseline,decoration=brace]
    matrix (m) [table] {
        1 & 0 & cdots & 0 & & 1 & 1 & cdots & 1 
        0 & 1 & cdots & 0 & & 0 & 0 & cdots & 0 
        vdots & vdots &  ddots & 0 & & vdots & vdots &ddots& vdots 
        0 & 0 & cdots & 1 & & 0 & 0 & cdots & 0 
        0 & 0 & cdots & 0 & & 1 & 0 & cdots & 1 
        0 & 0 & cdots & 0 &  & 0 & 1 & cdots & 0 
        vdots & vdots &  ddots & 0 & & vdots & vdots &ddots& vdots 
        1 & 1 & cdots & 1 & & 0 & 0 & cdots & 1 
    };
    node [above=.5em of m-1-1.north, anchor=south] {$a_{1n}$};
    node [above=.5em of m-1-2.north, anchor=south] {$a_{2n}$};
    node [above=.5em of m-1-3.north, anchor=south] {$ldots$};
    node [above=.5em of m-1-4.north, anchor=south] {$a_{mn}$};
    node [above=.5em of m-1-6.north, anchor=south] {$a_{11}$};
    node [above=.5em of m-1-7.north, anchor=south] {$a_{12}$};
    node [above=.5em of m-1-8.north, anchor=south] {$ldots$};
    node [above=.5em of m-1-9.north, anchor=south] {$a_{1n-1}$};
    draw[decorate,transform canvas={xshift=1.4em},thick] (m-1-9.north east) -- node[right=2pt] {$m$} (m-4-9.south east); % right
    draw[decorate,transform canvas={xshift=1.4em},thick] (m-5-9.north east) -- node[right=2pt] {$n$} (m-8-9.south east); % right
    draw[decorate,transform canvas={yshift=-.5em},thick] (m-8-4.south east) -- node[below=2pt] {$m$} (m-8-1.south west); % below
    draw[decorate,transform canvas={yshift=-.5em},thick] (m-8-9.south east) -- node[below=2pt] {$n-1$} (m-8-6.south west); % below
    draw [dotted] (m-1-5.north) -- (m-8-5.south);
    draw [dotted] (m-4-1.south west) -- (m-4-9.south east);
    end{tikzpicture}
    ]
    
    $A''=begin{pNiceMatrix}[first-row,%
    code-before =
    {
        tikz draw[decorate, decoration=brace,transform canvas={xshift=1.4em},thick] (row-1-|col-10) -- node[right=2pt] {$m$} (row-5-|col-10); % right
        tikz draw[decorate, decoration=brace,transform canvas={xshift=1.4em},thick] (row-5-|col-10) -- node[right=2pt] {$n$} (row-9-|col-10); % right
        tikz draw[decorate, decoration=brace,transform canvas={yshift=-.5em},thick] (row-9-|col-5) -- node[below=2pt] {$m$} (row-9-|col-1); % below
        tikz draw[decorate, decoration=brace,transform canvas={yshift=-.5em},thick] (row-9-|col-10) -- node[below=2pt] {$n-1$} (row-9-|col-6); % below
    }
    ]
        a_{1n} & a_{2n} & Cdots & a_{mn} && a_{11} & a_{12} & Cdots & a_{1n-1}
        1 & 0 & Cdots & 0 & Vdotsfor{8} & 1 & 1 & Cdots & 1
        0 & 1 & Cdots & 0 &              & 0 & 0 & Cdots & 0
        Vdots & Vdots & Ddots & Vdots & & Vdots & Vdots & Ddots & Vdots
        0 & 0 & Cdots & 1 & & 0 & 0 & Cdots & 0
        hdottedline
        0 & 0 & Cdots & 0 & & 1 & 0 & Cdots & 0
        0 & 0 & Cdots & 0 & & 0 & 1 & Cdots & 0
        Vdots & Vdots & Ddots & Vdots & & Vdots & Vdots & Ddots & Vdots
        1 & 1 & Cdots & 1 & & 0 & 0 & Cdots & 1
    end{pNiceMatrix}$
    
end{document}

Result