If ω is a complex cube root of unity, show that ([[1, ω, ω^2], [ω, ω^2, 1], [ω^2, 1, ω]] + [[ω, ω^2, 1], [ω^2, 1, ω], [ω^2, 1, ω], [ω, ω^2, 1]]) [[1], [ω], [ω^2]] = [[0], [0], [0]]