Value of determinant
`|[2,2 omega,omega^(2)],[omega,1,omega^(2)],[omega^(2),1,omega]|`

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

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

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)|.

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

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)|

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

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

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