`|(1,omega^2,1+omega^2),(1+omega^2,1,omega^2),(omega^2,1+omega^2,1)| = `

If omega is a cube root of unity , then |(x+1 , omega , omega^2),(omega , x+omega^2, 1),(omega^2 , 1, x+omega)| =

If 1,omega,omega^2 are the cube roots of unity , then Delta=|(1,omega^n, omega^2n),(omega^n , omega^(2n), 1),(omega^(2n), 1, omega^n)| is equal to :

Evaluate |(1,omega,omega^2),(omega,omega^2,1),(omega^2,omega,omega)| where omega is cube root of unity.

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)]

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