Question

Find cofactors of $A=\left[\begin{array}{ccc}2& 1& 3\\ 4& -1& 0\\ -7& 2& 1\end{array}\right]$

Answer 1

If $A$ is a square matrix, then the minor of the entry in the $i^{th}$ row and $j^{th}$ column (also called the $(i,j)$ minor, or a first minor) is the determinant of the submatrix formed by deleting the $i^{th}$ row and $j^{th}$ column. This number is often denoted $M_{i,j}$.
Minor is
$\left|\begin{array}{ccc}-1& 4& 1\\ -5& 23& 11\\ 3& -12& -6\end{array}\right|$
Cofactors is
A different type of cofactor, sometimes called a cofactor matrix, is a signed version of a minor $M_{\left(ij\right)}$ defined by
$C_{ij}=(-{)}^{i+j}{M}_{ij}$
$\left|\begin{array}{ccc}-1& -4& 1\\ 5& 23& -11\\ 3& 12& -6\end{array}\right|$