Make a symbol take up an entire (multi-column, multi-row) sub-matrix

Question

I'm trying to combine multirow and multicolumn to create a matrix with a 3x3 sub-matrix, which is labeled by a large symbol. Here is what I have so far:

\documentclass[10pt]{article}
\usepackage{fullpage, amsmath, amsthm, amsfonts}
\usepackage{multirow}
\begin{document}

\begin{equation*}
\tilde{\Gamma} = 
\left[
\begin{array}{cccc}
    \multicolumn{3}{c}{\multirow{3}{*}{A}} & 1 \\
    \multicolumn{3}{c}{} & \vdots  \\
    \multicolumn{3}{c}{} & 1 \\
    1 & \ldots & 1 & 0 \\
\end{array} \right]
\end{equation*}

\end{document}

There are two issues I would like to fix:

1) Is it possible to make the A take up the whole (or a larger part of) the block matrix?

2) This no longer works when I replace A with \Gamma.

Answer 1

Here's an option:

\documentclass{article}

\usepackage{graphicx}

\begin{document}

\[
  B = 
  \left[ \begin{array}{ *{4}{c} }
    & & & 1 \\
    & & & \vdots  \\
    \multicolumn{3}{c}
      {\raisebox{\dimexpr\normalbaselineskip+.7\ht\strutbox-.5\height}[0pt][0pt]
        {\scalebox{3}{$A$}}} & 1 \\
    1 & \cdots & 1 & 0
  \end{array} \right]
\]

\end{document}

The calculation of the positioning doesn't have to be that exact.