If AAA is a 3×33 \times 33×3 matrix such that A3=IA^3 = IA3=I and A≠IA \neq IA=I, what are the possible eigenvalues?
1,ω,ω21, \omega, \omega^21,ω,ω2 where ω=ei2π/3\omega = e^{i 2\pi/3}ω=ei2π/3
1,1,11, 1, 11,1,1
1,−1,11, -1, 11,−1,1
0,1,−10, 1, -10,1,−1