If `w` is cube roots of unity then `|[1,-omega,omega^(2)],[-omega,omega^(2),1],[omega^(2),1,-omega]|`=?

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 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 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 roots of unity, then Delta=|(1,omega^n,omega^(2n)),(omega^n,omega^(2n),1),(omega^(2n),1,omega^n)| is equal to

If omega is a complex cube root of unity, show 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 a cube root of unity, then omega + omega^(2)= …..

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

If omega(ne1) is a cube root of unity, then (1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8)) …upto 2n is factors, is

If omega is a cube root of unity, then 1+omega = …..

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