If $A=\begin{bmatrix}2 & 1 & 0 \\ 3 & 1 & 2 \\ 0 & 4 & -1\end{bmatrix}$, then $|adj(A)|$ is equal to:

First find $|A|$. $|A|=\begin{vmatrix}2 & 1 & 0 \\ 3 & 1 & 2 \\ 0 & 4 & -1\end{vmatrix}$ Expand along first row: $|A|=2\begin{vmatrix}1 & 2 \\ 4 & -1\end{vmatrix}-1\begin{vmatrix}3 & 2 \\ 0 & -1\end{vmatrix}$ $=2(1(-1)-2\times4)-1(3(-1)-0)$ $=2(-1-8)-(-3)$ $=-18+3$ $=-15$ Property: $|adj(A)|=|A|^{n-1}$ Here $n=3$. $|adj(A)|=(-15)^{2}=225$