## Differential Equations and Linear Algebra (4th Edition)

$-4.5$.
If $A$ and $B$ are $n\times n$ matrices, then $det(AB)=det(A)det(B)$. Also $det(A^T)=det(A)$ and if $det(A)\ne0$, then $det(A^{-1})=\frac{1}{det(A)}$ Hence here $det(B^2A^{-1})=det(B^2)det(A^{-1})=det(B)det(B)\frac{1}{det(A)}=3\cdot3\frac{1}{-2}=-4.5$.