Chapter 12 - Matrices - 12-3 Determinants and Inverses - Practice and Problem-Solving Exercises - Page 788: 14

$-0.75$

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} 0&0.5\\1.5&2 \end{bmatrix}$ is \begin{align*} & 0(2)-1.5(0.5) \\&= 0-0.75 \\&= -0.75 .\end{align*}