If `omega` is a complex cube root of unity, show that `([1omegaomega^2omegaomega^2 1omega^2 1omega]+[omegaomega^2 1omega^2 1omegaomegaomega^2 1])[1omegaomega^2]=[0 0 0]`

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)]=[000]

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

If omega is a cube root of unity, prove that (1+omega-omega^2)^3-(1-omega+omega^2)^3=0

If omega is a complex cube root of unity, then (1-omega+omega^(2))^(6)+(1-omega^(2)+omega)^(6)=

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 be an imaginary cube root of unity,show that (1+omega-omega^(2))(1-omega+omega^(2))=4

omega is a complex cube root of unity,then (1-omega)(1-+-ega^(2))(1-omega^(4))(1-omega^(8))

If omega is complex cube root of unity (1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8))(1-omega^(8)+omega^(16))