If `omega` is a complex cube root of unity. Show that `Det[[1,omega,omega^2 ],[omega,omega^2,1],[omega^2,1,omega]]=0`

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 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]]

If omega is a complex cube root of unity, show that (1+omega-omega^2)^6 = 64

If omega is a complex cube root of unity then a root of the equation |[x+1,omega,omega^2],[omega,x+omega^2,1],[omega^2,1,x+omega]|=0 is

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, show that (2+omega+omega^2)^3 - (1-3omega+omega^2)^3 =65

If omega is a complex cube root of unity , then the matrix A = [(1,omega^(2),omega),(omega^(2),omega,1),(omega,1,omega^(2))] is a :

If omega is a complex cube root of unity then the matrix A = [(1, omega^(2),omega),(omega^(2),omega,1),(omega,1,omega^(2))] is a

if omega!=1 is a complex cube root of unity, and x+iy=|[1,i,-omega],[-I,1,omega^2],[omega,-omega^2,1]|

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)]=[000]