Prove that `|[1,w^2,w^2],[w^2,1,w],[w^2,w,1]|=-3w` where w is a cube root of unity.

Prove that (1+w)(1+w^2)(1+w^4)(1+w^8)=1 where w is the imagination 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.

find the value of |[1,1,1],[1,omega^(2),omega],[1,omega,omega^(2)]| where omega is a 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,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.

Evaluate |(1, omega, omega^(2)),(omega, omega^(2),1),(omega^(2),1,omega)| , where omega is a 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 .

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