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

Let omega!=1 be a cube root of unit and Delta=|(1-omega-omega^(2),2,2),(2omega, omega-omega^(2)-1,2omega),(2omega^(2),2omega^(2),omega^(2)-1-omega)| then Delta equals

Prove that (1-omega-omega^(2))(1-omega+omega^(2))(1+omega-omega^(2))=8

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

If omega is a cube root of unity,then find the value of the following: (1+omega-omega^(2))(1-omega+omega^(2))

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

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

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

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