## Linear Algebra: A Modern Introduction

$-\frac{3}{2}$
We know that if $A$ and $B$ are $n\times n$ matrices, then $det(AB)=det(A)det(B)$. We also know that if $A$ is invertible, then $det(A^{-1})=\frac{1}{det(A)}$ Hence $det(B^{-1}A)=det(B^{-1})det(A)=\frac{1}{det(B)}det(A)=\frac{1}{-2}\cdot3=-\frac{3}{2}$