If `omega` is the cube root of unity, prove that `|[1,omega^6,omega^8],[omega^6,omega^3,omega^7],[omega^8,omega^7,1]|=3`

If omega is the cube root of unity,prove that det[[omega^(6),omega^(3),omega^(8)omega^(8),omega^(7),1]]=3

If omega is the cube root of unity then find the value of |[1,omega^(6),omega^(8)],[omega^(6),omega^(3),omega^(7)],[omega^(8),omega^(7),1]|

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

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!=1) is a cube root of unity then omega^(5)+omega^(4)+1 is

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