|[1,omega,omega^(2)],[omega,omega^(2),1],[omega^(2),1,omega]|quad [" Hint : "I+omega+omega^(2)=0]

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

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))

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]]

Prove 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):}] where omega is the cube root of unit.

{[(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))]

IF omega is cube root of unity, then |{:(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega):}| = ………. (1,0,omega, omega^2)

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

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