\begin{definition}[Definition:Cofactor Matrix]
Let $\mathbf A = \sqbrk a_n$ be a square matrix of order $n$.
Let $A_{r s}$ denote the cofactor of the element whose indices are $\tuple {r, s}$.
The '''cofactor matrix''' of $\mathbf A$ is the square matrix of order $n$:
:$\mathbf C = \begin {bmatrix}
A_{1 1} & A_{1 2} & \cdots & A_{1 n} \\
A_{2 1} & A_{2 2} & \cdots & A_{2 n} \\
 \vdots &  \vdots & \ddots &  \vdots \\
A_{n 1} & A_{n 2} & \cdots & A_{n n} \\
\end {bmatrix}$
\end{definition}