\begin{definition}[Definition:Adjugate Matrix]
Let $\mathbf A = \sqbrk a_n$ be a square matrix of order $n$.
Let $\mathbf C$ be its cofactor matrix.
The '''adjugate matrix''' of $\mathbf A$ is the transpose of $\mathbf C$:
:$\adj {\mathbf A} = \mathbf C^\intercal$
\end{definition}