`|(x,omega^2,omega),(omega,x,omega^2),(omega^2,omega,x)|`

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

If omega is an imaginary cube root of unity, then a root of equation |(x+1,omega,omega^2),(omega,x+omega^2,1),(omega^2,1,x+2)|=0,can be

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)]

If omegais an imaginary cube root of unity, then the value of the determinant |(1+omega,omega^2,-omega),(1+omega^2,omega,-omega^2),(omega+omega^2,omega,-omega^2)|