If $(w \neq 1)$ is a cube root of 1 then $\begin{bmatrix} 1 & 1+i+\omega^2 & \omega^2 \\ 1-i & -1 & \omega^2-1 \\ -1 & -i+\omega-1 & -1 \end{bmatrix}$ is a

Question

$\begin{array}{1 1} 0 \\ 1 \\ i \\ \omega \end{array}$