Chapter 12 - Matrices - 12-3 Determinants and Inverses - Practice and Problem-Solving Exercises - Page 788: 16

$-17$

The determinant of a $2\times2$ matrix $A=\begin{bmatrix}a & b\\c&d \end{bmatrix}$ is given by $ad-bc.$ Hence, the determinant of the given matrix, $ \begin{bmatrix} -1&3\\5&2 \end{bmatrix}$ is \begin{align*}\require{cancel} & -1(2)-5(3) \\&= -2-15 \\&= -17 .\end{align*}