Answer
$-25$
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:
$$det= \begin{vmatrix} a_{11} & a_{12} \\
a_{21} & a_{22} \\ \end{vmatrix}=a_{11}a_{22}-a_{12}a_{21}$$
Using the formula above gives,
$$\begin{vmatrix} -1 & 8 \\
2 & 9 \\ \end{vmatrix}=(-1)(9) -(2)(8) \\=-9-16 \\=-25$$
Therefore, the determinant is: $-25$.
