If $\vec a,\vec b,\vec c$ are non-coplanar non-null vectors such that $[\vec a\,\,\vec b\,\,\vec c]=2$ then $\left\{\begin{bmatrix}\vec a×\vec b &\vec b×\vec c& \vec c×\vec a\end{bmatrix}\right\}^2=$

16

We have,

$\left\{\begin{bmatrix}\vec a×\vec b &\vec b×\vec c& \vec c×\vec a\end{bmatrix}\right\}^2=\left\{[\vec a\,\,\vec b\,\,\vec c]\right\}^4=2^4=16$