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{[(1,omega,omega^(2)),(omega,omega^(2),1...

`{[(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))]`

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

|[1,omega,omega^2] , [omega, omega^2,1] , [omega^2,1,omega]|=0

|[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]] =

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

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

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