Simplify `|[1,omega^3,omega^2],[omega^3,1,omega],[omega^2,omega,1]|`

|[1,omega,omega^2] , [omega, omega^2,1] , [omega^2,1,omega]|=0

If omega is non-real cube root of unity and matrix P= [[1,omega^(3),omega^(2)],[omega,1,omega],[omega^(2),omega,1]] then det(p) =

If omega is cube root of unit, then find the value of determinant |(1,omega^3,omega^2), (omega^3,1,omega), (omega^2,omega,1)|.

If omega is cube roots of unity, prove that {[(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega)]+[(omega,omega^2,1),(omega^2,1,omega),(omega,omega^2,1)]} [(1),(omega),(omega^2)]=[(0),(0),(0)]

det [[1, omega, omega^(2) omega, omega^(2), 1omega^(2), 1, omega]]

{[(1,omega,omega^(2)),(omega,omega^(2),1),(omega^(2),1,omega)] + [(omega,omega^(2),1),(omega^(2),1,omega),(omega,omega^(2),1)]} [(1),(omega),(omega^(2))]

|[omega+omega^(2),1,omega],[omega^(2)+1,omega^(2),1],[1+omega,omega,omega^(2)]|