Determinants & Inverses · Challenge problem

Vectors $\mathbf u, \mathbf v, \mathbf w$ in $\mathbb R^3$ satisfy $\det[\mathbf u\ \mathbf v\ \mathbf w] = 3$. Find the volume of the parallelepiped spanned by $\mathbf u \times \mathbf v$, $\mathbf v \times \mathbf w$ and $\mathbf w \times \mathbf u$.