# How can I write description/text beside matrix as shown?

How can I achieve this in LaTeX?

Your question is probably a duplicate of this one, but I like to show you an alternative solution with tikzmark.

\documentclass{article}
\usepackage{amsmath}
\usepackage{array}
\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing}
\usetikzlibrary{tikzmark, calc}

\newcommand{\mybrace}[3]{%
\draw[decorate,decoration={brace,mirror}]
($(pic cs:#1)+(-.3,.3)$) -- node[xshift=-1em, align=left, text width=4em]{#3} ($(pic cs:#2)+(-.3,-.1)$);}

\renewcommand*{\arraystretch}{1.25}

\begin{document}
$\begin{bmatrix} \tikzmark{lp} P \\ \tikzmark{lq} Q \\ \tikzmark{gp} P \\ \tikzmark{gq} Q \\ \end{bmatrix}$
\begin{tikzpicture}[overlay,remember picture,baseline]