TikZ : Drawing a Triangular Block Matrix

You can use the points relative to the nodes to draw the sectors, even leaving space for the delimiters to be seen at different distances, you can uncomment line 30 to see the nodes that delimit the coordinates relative to the nodes. I do not know if it is the most practical but it is an adaptation that comes to resemble what you want.

MWE:

\documentclass[tikz,border=14pt]{standalone}
\usepackage{tikz}  
\usetikzlibrary{matrix,shapes,decorations.pathreplacing}

\begin{document}
    \begin{tikzpicture}[
        %Global config
        >=latex,
        line width=1pt,
        %Styles
        Brace/.style={
            decorate,
            decoration={
                brace,
                raise=-7pt
            }
        }
    ]

    \matrix[% General option for all nodes
        matrix of nodes,
        text height=2.5ex,
        text depth=0.75ex,
        text width=3.25ex,
        align=center,
        left delimiter=(,
        right delimiter= ),
        column sep=5pt,
        row sep=5pt,
        %nodes={draw=black!10}, % Uncoment to see the square nodes.
        nodes in empty cells,
    ] at (0,0) (M){ % Matrix contents  
    &   \huge 0&   &   &   &   &  \\
    &   &   &   &   &   &  \\
    &   &   &   &   &   &  \\
    &   &   &   &   &   &  \\
    &   &   &   &   &   &  \\
    &   &   &   &   &   & \huge 0 \\
    };
% Drawing the sectors using matrix coordinate names.    
    \draw[thick] (M-1-2) -- (M-6-7);
    \draw[thick,fill=red!30,draw] (M-1-3.center)
    -- (M-4-6.center)
    -- (M-1-6.center)
    -- cycle;
    \draw[thick,fill=red!30,draw] (M-2-2.center)
    -- (M-5-2.center)
    -- (M-5-5.center)
    -- cycle;
    \draw[thick,fill=yellow!30,draw](M-1-6.east)
    -- (M-1-7.center)
    -- (M-5-7.center)
    -- (M-4-6.south east)
    -- cycle;
    \draw[thick,fill=yellow!30,draw](M-5-2.south)
    -- (M-5-5.south east)
    -- (M-6-6.center)
    -- (M-6-2.center)
    -- cycle;
% Drawing the braces.   
    \draw[Brace] (M-1-3.north)
    -- (M-1-6.north)
    node[midway,above]{$x-y$};
    \draw[Brace] (M-1-6.north east)
    -- (M-1-7.north)
    node[midway,above]{$y$};

    \draw[Brace] (M-5-2.west)
    -- (M-2-2.west)
    node[midway,left]{$x-y$};

    \draw[Brace] (M-6-2.west)
    -- (M-5-2.south west)
    node[midway,left]{$y$};
% Labeling the sectors  
    \node at (M-4-3){\sf A};
    \node at (M-2-5){\sf A};
    \draw (M-3-7)++(-8pt,0) node {\sf B};
    \draw (M-6-4)++(0,8pt) node {\sf B};

    \end{tikzpicture}
\end{document}

You already load the relevant libraries and even have a style that does what you want. You only need to use them.

\documentclass[letterpaper,11pt]{article}

\usepackage{tikz}
\usepackage{ifthen}
\usetikzlibrary{matrix}
\usetikzlibrary{decorations.pathreplacing}
\begin{document}
\begin{tikzpicture}
\matrix[matrix of math nodes,
left delimiter=(,
right delimiter=),
nodes in empty cells] (m)
{
    &   &   &   &   &  \\
    &   &   &   &   &  \\
    &   &   &   &   &  \\
    &   &   &   &   &  \\
    &   &   &   &   &  \\
    &   &   &   &   &  \\
};
\fill[yellow!30] (m.north west) |- (m-6-6.south east);
\fill[yellow!30] (m.north west) -| (m-6-6.south east);
\fill[red!30] (m.north west) -| (m-4-4.south east);
\fill[red!30] (m.north west) |- (m-4-4.south east);
\draw[line width=3mm,white]  (m.north west) -- (m-6-6.south east);

\draw[thick,-] (m-1-1.north west) -- (m-6-6.south east);
\node [fill=white, outer sep=0,inner sep=1,minimum size=3] at (m-1-1.north west) {0};
\node [fill=white, outer sep=0,inner sep=1,minimum size=10] at  (m-6-6.south east) {0};
\tikzset{myedgestyle/.style={decorate, decoration={brace,raise=4pt}}}
\draw[myedgestyle] (m-1-2.north west) -- (m-1-4.north east)
node[midway,above=3pt,font=\tiny]{$x-y$};
\draw[myedgestyle] (m-1-5.north west) -- (m-1-6.north east)
node[midway,above=3pt,font=\tiny]{$y$};
\draw[myedgestyle] ([xshift=-8pt]m-6-1.south west) -- ([xshift=-8pt]m-5-1.north west)
node[midway,left=3pt,font=\tiny]{$y$};
\draw[myedgestyle] ([xshift=-8pt]m-4-1.south west) -- ([xshift=-8pt]m-1-1.north west)
node[midway,left=3pt,font=\tiny]{$x-y$};
\end{tikzpicture}
\end{document}