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

What is the value of |(1-i, omega^2,-omega), (omega^2+i,omega,-i), (1-2i-omega^2,omega^2-omega,i-omega)|, where omega is the cube root of unity?

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

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

Evaluate: | (1, 1, 1), (1, omega^2, omega), (1, omega, omega^2)| (where omega is an imaginary cube root unity).

What is the value of |{:(" "1-i," "omega^(2)," "-omega),(" "omega^(2)+i," "omega," "-i),(1-2i-omega^(2),omega^(2)-omega,i-omega):}| , where omega is the cube root of unity ?

What is the value of |(1,omega,2 omega^(2)),(2,2omega^(2),4 omega^(3)),(3,3 omega^(3),6 omega^(4))| , where omega is the cube root of the unity ?