Answer
$7$
Work Step by Step
By using the cofactor expansion along the first row:
$det\begin{vmatrix}
1&1 &-1\\
2&0 &1\\
3&-2 &1
\end{vmatrix}$
$=+1\times det\begin{vmatrix}
0&1\\
-2&1
\end{vmatrix}-1\times det\begin{vmatrix}
2 &1\\
3&1
\end{vmatrix}+(-1)\times det\begin{vmatrix}
2&0\\
3&-2
\end{vmatrix}$
$=1(0+2)-1(2-3)-1(-4-0)$
$=2+1+4$
$=7$
