\begin{definition}[Definition:Adjugate]
Let:
: $D = \begin{vmatrix}  a_{11} & a_{12} & \cdots & a_{1n} \\
  a_{21} & a_{22} & \cdots & a_{2n} \\
\vdots & \vdots & \ddots & \vdots \\
  a_{n1} & a_{n2} & \cdots & a_{nn}\end{vmatrix}$
be a determinant of order $n$.
Let $a_{rs}$ be an element of $D$.
Let $A_{rs}$ be the cofactor of $a_{rs}$ in $D$.
Then the determinant:
: $D^* = \begin{vmatrix}  A_{11} & A_{12} & \cdots & A_{1n} \\
  A_{21} & A_{22} & \cdots & A_{2n} \\
\vdots & \vdots & \ddots & \vdots \\
  A_{n1} & A_{n2} & \cdots & A_{nn}\end{vmatrix}$
is called the '''adjugate (determinant)''' of $D$.
\end{definition}