If w is a complex cube root of unity, show that `([[1,w,w^2],[w,w^2,1],[w^2,1,w]]+[[w,w^2,1],[w^2,1,w],[w,w^2,1]])*[[1],[w],[w^2]]=[[0],[0],[0]]`

If w is a complex cube root of unity. Show that |[1,w, w^2],[w, w^2, 1],[w^2, 1,w]|=0 .

If w is the imaginary cube root of unity evaluate |(1,w,w^2),(w,w^2,1),(w^2,1,w)|

If w is an imaginary cube root of unity, find the value of |[1,w, w^2],[ w ,w^2 ,1],[w^2 ,1,w]| .

If w is a complex cube root unity then |{:(1,1+w,1+w^(2)),(1+w,1+w^(2),1),(1+w^(2),1,1+w):}|=

If omega is a complex cube root of unity, show that (1+omega)^3 - (1+omega^2)^3 =0

If omega is a complex cube root of unity, then (1-omega+(omega)^2)^3 =

If omega is a complex cube root of unity, show that [[1 , omega, omega^2], [ omega, omega^2, 1],[ omega^2, 1, omega]] [[1],[ omega],[ omega^2]]=[[0],[ 0],[ 0]]

If w is a complex cube root of unity, then show that (1-w) (1- w ^(2)) (1 - w ^(4)) ( 1 - w ^(5)) = 9

If omega is a complex cube root of unity, show that ([[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]]=[[0, 0 ,0]]