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

Question

$\begin{array}{1 1} (1) z \\ (2) −1 \\ (3) 1 \\ (4) −z \end{array} $