Linear Algebra

For an $n \times n$ matrix $A$: $\det(k A^{-1}) = k^n \det(A^{-1}) = \frac{k^n}{\det(A)}$ Here $n = 3$, $k = 2$, and $\det(A) = 5$: $\det(2 A^{-1}) = \frac{2^3}{\det(A)} = \frac{8}{5} = 1.6$