Answer
$-3$
Work Step by Step
The determinant for a $2 \times 2$ matrix $\begin{bmatrix} a_{11} & a_{12} \\
a_{21} & a_{22} \\ \end{bmatrix}$ can be defined as:
$\text{det}= \begin{vmatrix} a_{11} & a_{12} \\
a_{21} & a_{22} \\ \end{vmatrix}=a_{11}a_{22}-a_{12}a_{21}$
Therefore,
$\text{det}=\begin{vmatrix} -1 & 3 \\
-2 & 9 \\ \end{vmatrix}=(-1)(9) -(3)(-2) \\=-9+6 \\ =-3$
Therefore, the determinant of the given matrix is: $-3$
