If $\det \mathbf{A} = 4$ and $\det \mathbf{B} = -5,$ then find $\det (\mathbf{A} \mathbf{B}).$
I know that the determinant of a product of two matrices is equal to the product of their determinants, as long as they are both square matrices of the same size. So, $\det (\mathbf{A} \mathbf{B}) = \det \mathbf{A} \det \mathbf{B} = 4 \cdot (-5) = -20.$ 