#### Answer

$1-\ln x$

#### 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:
$det =(x)(\dfrac{1}{x})-\ln x$
or, $=1-\ln x$