For $A = \begin{bmatrix}1 & 2 & 0 \\ 3 & -1 & 4 \\ 2 & 0 & 5\end{bmatrix}$, what is the element in row 1, column 2 of $\operatorname{adj} A$?

Explanation

1. 01

   $\operatorname{adj} A$ is the transpose of the matrix of cofactors, so its $(1, 2)$ element is the cofactor $A_{21}$.

2. 02

   $A_{21} = (-1)^{2 + 1}\begin{vmatrix} 2 & 0 \\ 0 & 5 \end{vmatrix} = -10$.