Chapter 12 - Matrices - 12-3 Determinants and Inverses - Practice and Problem-Solving Exercises - Page 788: 18

$-3$

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} 2&-1\\5&-4 \end{bmatrix}$ is \begin{align*}\require{cancel} & 2(-4)-5(-1) \\&= -8+5 \\&= -3 .\end{align*}