`|(1,omega,1+omega),(1+omega,1,omega),(omega,1+omega,1)| = `

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)|.

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 complex cube root of unity then the value of the determinant |[1,omega,omega+1] , [omega+1,1,omega] , [omega, omega+1, 1]| is

{[(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))]

If omega is a complex cube root of unity then the matrix A = [(1, omega^(2),omega),(omega^(2),omega,1),(omega,1,omega^(2))] is a

Suppose omega!=1 is a sube root of unity, and Delta=|(1,omega^(2),1-omega^(4)),(omega,1,1+omega^(5)),(1,omega,omega^(2))| then |Re(Delta)|= _____________