Suppose that $A$ is an $n\times n$ matrix and that the entry in the $i$th row and $j$th column of $A$ is given by $a_{ij}$. To compute the determinant of $A$ using a cofactor expansion across the $i$th row we calculate:

$$\det(A)=a_{i1} C_{i1}+a_{i2} C_{i2}+\ldots +a_{in}C_{in}$$

What is $C_{ij}$?