Find whether
`|(1,omega,omega^2),(omega,1,1),(omega^2,1,omega)| = 0?`

|[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)]

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)|.

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.

(1-omega+omega^(2))(1+omega-omega^(2))=4