The least value of the product xyz for which the determinant $\begin{bmatrix}x & 1 & 1\\1 & y & 1\\1 & 1 & z\end{bmatrix}$ is non-negative , is :

Question

$\begin{array}{1 1} -2 \sqrt 2 \\ -16 \sqrt 2 \\ -8 \\ -1 \end{array} $