([[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]]

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

|[omega+omega^(2),1,omega],[omega^(2)+1,omega^(2),1],[1+omega,omega,omega^(2)]|

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]

(1+omega-omega^(2))(1-omega+omega^(2))

det [[1, omega, omega^(2) omega, omega^(2), 1omega^(2), 1, omega]]

det [[1, omega, omega^(2) omega, omega^(2), 1omega^(2), 1, omega]] =

(1-omega+omega^(2))(1+omega-omega^(2))=4

(1-omega +omega^2)(1+omega-omega^2)=4

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