Answer
$\det ((B)^{-1}(A)^{-1})=\frac{1}{15}$
Work Step by Step
Since $A$ and $B$ are $4 \times 4$ matrix, applying the property $P9$, we obtain:
$\det ((B)^{-1}(A)^{-1})=\det (B)^{-1}.\det (A)^{-1}$
Solve both determinants by applying property $P10$:
$\det (B)^{-1}=\frac{1}{\det (B)}=\frac{1}{3}$
$\det (A)^{-1}=\frac{1}{\det (A)}=\frac{1}{5}$
Hence, $\det ((B)^{-1}(A)^{-1})=\frac{1}{3}.\frac{1}{5}=\frac{1}{15}$
