Answer
$-6$
Work Step by Step
The determinant for a $2 \times 2$ matrix $\begin{bmatrix} a_{11} & a_{12} \\
a_{21} & a_{22} \\ \end{bmatrix}$ is defined as:
$$\begin{vmatrix} a_{11} & a_{12} \\
a_{21} & a_{22} \\ \end{vmatrix}=a_{11}a_{22}-a_{12}a_{21}$$
Using the formula above gives:
$$\begin{vmatrix} -2 & 4 \\
0 & 3 \\ \end{vmatrix}=(-2)(3) -(4)(0) \\=-6-0 \\=-6$$
Therefore, the determinant of a given matrix is: $-6$.
