For $\begin{vmatrix} 5 & -2 \\ 3 & 7 \end{vmatrix}$, what is the cofactor $A_{12}$ of the element $-2$?

Explanation

1. 01

   Deleting row 1 and column 2 leaves 3, so the minor is $M_{12} = 3$.

2. 02

   $A_{12} = (-1)^{1 + 2}M_{12} = -3$.