# Definition:Cofactor Matrix

## Definition

Let $R$ be a commutative ring with unity.

Let $\mathbf A \in R^{n \times n}$ be a square matrix of order $n$.

Let $A_{r s}$ denote the cofactor of the $\tuple {r, s}$th entry.

The cofactor matrix of $\mathbf A$ is the square matrix

$\mathbf C = \begin {bmatrix} A_{1 1} & A_{1 2} & \cdots & A_{1 n} \\ A_{2 1} & A_{2 2} & \cdots & A_{2 n} \\ \vdots & \vdots & \ddots & \vdots \\ A_{n 1} & A_{n 2} & \cdots & A_{n n} \end {bmatrix}$

## Also known as

The cofactor matrix is also called comatrix or matrix of cofactors.