Chapter 12 - Matrices - 12-3 Determinants and Inverses - Practice and Problem-Solving Exercises - Page 789: 39

$-120$

The determinant of a $2\times2$ matrix $A=\begin{bmatrix}a & b\\c&d \end{bmatrix}$ is given by $ad-cb.$ Hence, the determinant of the given matrix, $ \begin{bmatrix} -3&10\\6&20 \end{bmatrix}$ is \begin{align*}\require{cancel} & -3(20)-6(10) \\&= -60-60 \\&= -120 .\end{align*}