Consider the matrix A=(1111ωω21ω2ω4)A = \begin{pmatrix} 1 & 1 & 1 \\ 1 & \omega & \omega^2 \\ 1 & \omega^2 & \omega^4 \end{pmatrix}A=1111ωω21ω2ω4 where ω=ei2π3\omega = e^{i \frac{2\pi}{3}}ω=ei32π. What is det(A)\det(A)det(A)?
000
333
3ω3\omega3ω
3ω23\omega^23ω2