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+% arara: pdflatex
+% arara: makeglossaries
+% arara: pdflatex
+\documentclass{article}
+
+\usepackage[T1]{fontenc}
+\usepackage{amsmath}
+\usepackage[colorlinks]{hyperref}
+\usepackage[postdot,style=index]{glossaries-extra}
+
+\makeglossaries
+
+\newcommand*{\mtx}[1]{\boldsymbol{#1}}
+\newcommand*{\mtxinv}[1]{\mtx{#1}\sp{-1}}
+
+\newglossaryentry{matrix}{%
+ name={matrix},
+ symbol={\ensuremath{\mtx{M}}},
+ plural={matrices},
+ user1={mtx},
+ description={rectangular array of values}
+}
+
+\newglossaryentry{identitymatrix}{%
+ name={identity matrix},
+ symbol={\ensuremath{\mtx{I}}},
+ plural={identity matrices},
+ description={a diagonal matrix with all diagonal elements equal to
+1 and all other elements equal to 0}
+}
+
+\newglossaryentry{matrixinv}{%
+ name={matrix inverse},
+ symbol={\ensuremath{\mtxinv{M}}},
+ user1={mtxinv},
+ description={a square \gls{matrix} such that
+ $\mtx{M}\mtxinv{M}=\glssymbol{identitymatrix}$}
+}
+
+\renewcommand{\GlsXtrFmtDefaultOptions}{hyper=false,noindex}
+
+\begin{document}
+A \gls{matrix} is denoted \glssymbol{matrix}.
+The inverse is denoted \glssymbol{matrixinv}.
+
+\newpage
+
+\[
+ \glsxtrfmt{matrix}{A}
+ \glsxtrfmt{matrixinv}{A}
+ =
+ \glssymbol{identitymatrix}
+\]
+
+\newpage
+
+\printglossaries
+\end{document}