Let $\omega$ be a complex number such that $2 \omega + 1 = z$ where $z = \sqrt{-3}$. If $\begin{vmatrix} 1 & 1& 1 \\ 1 & -\omega^2-1& \omega^2 \\ 1 & \omega^2 & \omega^7 \end{vmatrix} = 3k$, then $k$ is equal to :

Question

( A ) $-1$
( B ) $z$
( C ) $-z$
( D ) $1$