Answer
$-\dfrac{7}{16}$
Work Step by Step
The general formula to calculate the determinant of a $2 \times 2$ matrix which has 2 rows and 2 columns is
$D=\begin{vmatrix}a&b\\c&d\end{vmatrix}=ad-bc$
Now,
$D=\begin{vmatrix}\frac{1}{2}&\frac{1}{2}\\\frac{1}{8}&\frac{-3}{4}\end{vmatrix}=\frac{-3}{8}-\frac{1}{16}=-\dfrac{7}{16}$
