Show that `det ((1,omega,omega^2), (omega, omega^2,1),(omega^2,1,omega))=0` where `omega` is the non-real cube root of unity

|{:(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega):}|=0 where omega is an imaginary cube root of unity.

Evaluate |(1, omega, omega^(2)),(omega, omega^(2),1),(omega^(2),1,omega)| , where omega is a cube root of unity.

Evaluate |(1,omega,omega^2),(omega,omega^2,1),(omega^2,omega,omega)| where omega is cube root of unity.

Evaluate |(1,omega,omega^2),(omega,omega^2,1),(omega^2,omega, omega)| where omega is cube root of unity.

Using properties, prove that |[1,omega,omega^2],[omega,omega^2,1],[omega^2,1,omega]|=0 where omega is a complex cube root of unity.

Evaluate abs((1,omega,omega^2),(omega^2,1,omega),(omega^2,omega,1)) were omega is an imaginary cube root of unity.

Prove that the value of determinant |{:(1,,omega,,omega^(2)),(omega ,,omega^(2),,1),( omega^(2),, 1,,omega):}|=0 where omega is complex cube root of unity .

Prove that the value of determinant |{:(1,,omega,,omega^(2)),(omega ,,omega^(2),,1),( omega^(2),, 1,,omega):}|=0 where omega is complex cube root of unity .

Evalute: |{:(1,omega^3,omega^2),(omega^3,1,omega),(omega^2,omega,1):}| , where omega is an imaginary cube root of unity .

Find the value of |{:(" "1+i," "i omega," "i omega^(2)),(" "i omega," "i omega^(2)+1," "i omega^(3)),(i omega^(2), i omega^(3), " "i omega^(4)+1):}| , where omega is a non real cube root of unity and i = sqrt(-1) .