Answer
$\text{determinant of }
\begin{bmatrix}
-2 & -3
\\
5 & 0
\end{bmatrix}
=
15$
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}
-2 & -3
\\
5 & 0
\end{bmatrix}
,$ is
\begin{align*}
&
-2(0)-5(-3)
\\&=
0+15
\\&=
15
.\end{align*}
Hence, the $
\text{determinant of }
\begin{bmatrix}
-2 & -3
\\
5 & 0
\end{bmatrix}
=
15
.$
