Submatrix and element alignment within matrix

Question

I'm having trouble aligning submatrices and elements within the same matrix. Essentially, what I want to do is this (excuse the terrible paint-job):

Where the submatrix Q is located at the middle of the upper-left four matrix cells. I'm primarily familiar with the array environment: is this a possibility there?

Answer 1

How about a matrix inside a matrix?

\documentclass{article}
\pagestyle{empty}% for cropping
\usepackage{amsmath}
\begin{document}
$
\begin{vmatrix}
    Q & \begin{matrix} 0 \\ 0 \end{matrix} \\
    \begin{matrix} 2 & 3 \end{matrix} & -1
\end{vmatrix}
$
\end{document}

Answer 2

Or

\documentclass{article}
\pagestyle{empty} % for cropping
\usepackage{amsmath}
\begin{document}
\[\left|
\begin{array}{cr}
    Q & \begin{matrix} 0 \\ 0 \end{matrix} \\
    \begin{matrix} 2 & 3 \end{matrix} & -1
\end{array}
\right|\]
\end{document}

using the array environment that allows a better alignment.

or maybe something like

\documentclass{article}
\pagestyle{empty} % for cropping
\usepackage{amsmath}
\usepackage{arydshln}
\begin{document}
  \[ \left|
    \begin{array}{c;{2pt/2pt}r}
    \mbox{\LARGE $Q$} & \begin{matrix} 0 \\ 0 \end{matrix} \\ \hdashline[2pt/2pt]
    \begin{matrix} 2 & 3 \end{matrix} & -1
    \end{array}
    \right|
  \]
\end{document}

that modifies the size of Q and includes dashed lines between columns using the arydshln package.

Answer 3

A third solution with \multicolumn and multirow. I defined a \block macro with two arguments: the number of rows and columns that the block takes up (expressed as a pair) and what it puts in the block:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{fourier, heuristica}
\usepackage{multirow}
\usepackage{mathtools}
\def\block(#1,#2)#3{\multicolumn{#2}{c}{\multirow{#1}{*}{$ #3 $}}}

\begin{document}

\[ \begin{vmatrix*}[r]
\block(2,2){Q} & 0 \\
     & & 0 \\
     2 & 3 & \mathllap{-}1
\end{vmatrix*} \]

\[ \begin{vmatrix*}[r]
2 & 3 & -1 & 0 \\
0 & \block(2,2){P} & 0 \\
  4 & & & 0 \\
3 &2 & 1 & 2
\end{vmatrix*} \]

\end{document} 

Answer 4

With {vNiceMatrix} of nicematrix.

\documentclass{article}
\usepackage{nicematrix}

\begin{document}

$\begin{vNiceMatrix}
\Block{2-2}<\Large>{Q} &   & 0 \\
                       &   & 0 \\
                     2 & 3 & -1 
\end{vNiceMatrix}$

\end{document}