How to edit this code to get these two variants?

Question

I have the following code

\documentclass[12pt]{article}
\usepackage{geometry}
\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing,calligraphy}
\begin{document}

    \begin{tikzpicture}[yscale=1,
    brace/.style={thick,decorate,
        decoration={calligraphic brace, amplitude=7pt,raise=0.5ex}}]
    \draw (0,0) coordinate (O) rectangle (9,3)  coordinate (TR)
    (3,3) coordinate (T) -- (3,0) coordinate (B) -- (0,3) 
    coordinate (TL)
    (0.4,0.4) node[above right,font=\Huge]{$\mathbf{0}$};
    \draw[brace] (O)    -- node[left=1.5ex]{$I_n^2$} (TL);
    \draw[brace] (TL)   -- node[above=1.5ex]{$I_n^2$} (T);
    \draw[brace] (T)    -- node[above=1.5ex]{$I_n^1$} (TR);
    \end{tikzpicture}
\end{document}

and its output

Could you please help me edit this code to achieve two below variants? This is the last part of my thesis. Thank you so much for your help!

and

Answer 1

This is an almost exact copy of my previous answer, with many similar posts existing on this site. One can decorate some paths with braces, draw some rectangles, and combine x and y components of coordinates a la https://tex.stackexchange.com/a/401429.

\documentclass[12pt]{article}
\usepackage{geometry}
\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing,calligraphy}
\begin{document}

\begin{tikzpicture}[yscale=0.7,
    brace/.style={thick,decorate,
        decoration={calligraphic brace, amplitude=7pt,raise=0.5ex}}]
\draw (0,0) coordinate (TL) rectangle (6,-4.5)  coordinate (BR)
    (TL) rectangle (3,-3)  coordinate (br)
    (TL) -- (br)
    (0.4,0.4-3) node[above right,font=\Huge]{$\mathbf{0}$};
 \draw[brace] (BR-|TL)  -- node[left=1.5ex]{$K$} (br-|TL);
 \draw[brace] (br-|TL)  -- node[left=1.5ex]{$I$} (TL);
 \draw[brace] (TL)  -- node[above=1.5ex]{$I$} (br|-TL);
 \draw[brace] (br|-TL)  -- node[above=1.5ex]{$J$} (BR|-TL);
\end{tikzpicture}

\bigskip

\begin{tikzpicture}[yscale=0.7,
    brace/.style={thick,decorate,
        decoration={calligraphic brace, amplitude=7pt,raise=0.5ex}}]
\draw (0,0) coordinate (TL) rectangle (4.5,-4.5)  coordinate (BR)
    (TL) rectangle (3,-3)  coordinate (br)
    (TL-|BR) rectangle (7.5,-4.5)  coordinate (BRR)
    (TL) -- (br)
    (0.4,0.4-3) node[above right,font=\Huge]{$\mathbf{0}$};
 \draw[brace] (BR-|TL)  -- node[left=1.5ex]{$J$} (br-|TL);
 \draw[brace] (br-|TL)  -- node[left=1.5ex]{$I$} (TL);
 \draw[brace] (TL)  -- node[above=1.5ex]{$I$} (br|-TL);
 \draw[brace] (br|-TL)  -- node[above=1.5ex]{$J$} (BR|-TL);
 \draw[brace] (BR|-TL)  -- node[above=1.5ex]{$K$} (BRR|-TL);
\end{tikzpicture}

\end{document}