Answer
$e^{-2x}$
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:
$det =(e^{-x})((1-x)e^{-x})+(e^{-x})x(e^{-x})$
or, $=e^{-2x}-xe^{-2x}+xe^{-2x}$
or, $=e^{-2x}$
