#### Answer

$x$

#### 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:
$det =(x)(1+\ln x)-x \ln x$
or, $=x+x \ln x -x \ln x$
or, $=x$