`|[x+w^2,w,1],[w,w^2,1+x],[1,x+w,w^2]|=0`

det[[x+w^(2),w,1w,w^(2),1+x1,x+w,w^(2)]]=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 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 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

|[1,omega,omega^2] , [omega, omega^2,1] , [omega^2,1,omega]|=0

Solve the following : [[x+1,omega,omega^2],[omega,x+omega^2,1],[omega^2,1,x+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]]+[[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], [ omega, omega^2, 1],[ omega^2, 1, omega]] [[1],[ omega],[ omega^2]]=[[0],[ 0],[ 0]]

If the cube roots of unity are 1,omega,omega^(2), then the roots of the equation (x-1)^(3)+8=0 are : (a)-1,1+2w,1+2w^(2)(b)-1,1-2w,1-2w^(2)(b)1,w,w^(2)