Precalculus (10th Edition)

$-2$
We know that for a matrix $\left[\begin{array}{rr} a & b \\ c &d \\ \end{array} \right]$ the determinant is $D=ad-bc.$ Hence, here we have $D=(-4\cdot3)-[2\cdot(-5)]\\ D=-12-(-10)\\ D=-12+10\\ D=-2$