Prove that
`|(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega)| = 0`

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)]

Given that [(1,omega,omega^(2)),(omega,omega^(2),1),(omega^(2),1,omega)][(k,1,1),(1,1,1),(1,1,1)]=[(0,0,0),(0,0,0),(0,0,0)] then k=

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

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 omega is a complex cube root of unity, then a root of the equation |(x +1,omega,omega^(2)),(omega,x + omega^(2),1),(omega^(2),1,x + omega)| = 0 , is

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 a complex cube root of unity.Show that Det[[1,omega,omega^(2)omega,omega^(2),1omega^(2),1,omega]]=0