Answer
$\text{determinant of }
\begin{bmatrix}
-\dfrac{1}{2} & 2
\\
-2 & 8
\end{bmatrix}
=
0$
Work Step by Step
Using the determinant of a $2\times2$ matrix $A=\begin{bmatrix}a&b\\c&d
\end{bmatrix}$ which is given by $ad-cb$ the determinant of the given matrix, $
\begin{bmatrix}
-\dfrac{1}{2} & 2
\\
-2 & 8
\end{bmatrix}
,$ is
\begin{align*}
&
\left(-\dfrac{1}{2}\right)(8)-(-2)(2)
\\\\&=
-4+4
\\&=
0
.\end{align*}
Hence, $
\text{determinant of }
\begin{bmatrix}
-\dfrac{1}{2} & 2
\\
-2 & 8
\end{bmatrix}
=
0
.$
