#### Answer

$8uv-1$

#### Work Step by Step

The determinant of a $2 \times 2$ matrix can be computed by using the formula $det =ps-qr$
where $det =\begin{bmatrix}p & q \\r & s\end{bmatrix}$
After simplifying, the determinant of this matrix will be:
$det =(4u)(2v) -(-1) (-1) $
or, $=8uv-1$