JEE Math Practice Question

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

1. A.z
2. B.-1
3. C.1
4. D.-z