\begin{definition}[Definition:Cofactor/Element]
Let:
:$D = \begin {vmatrix}
a_{1 1} & a_{1 2} & \cdots & a_{1 n} \\
a_{2 1} & a_{2 2} & \cdots & a_{2 n} \\
 \vdots &  \vdots & \ddots &  \vdots \\
a_{n 1} & a_{n 2} & \cdots & a_{n n} \\
\end {vmatrix}$
be a determinant of order $n$.
Let $a_{r s}$ be an element of $D$.
Let $D_{r s}$ be the determinant of order $n-1$ obtained from $D$ by deleting row $r$ and column $s$.
Then the '''cofactor''' $A_{r s}$ of the element $a_{r s}$ is defined as:
:$A_{r s} := \paren {-1}^{r + s} D_{r s}$
\end{definition}