" (xiv) "|[1,omega,omega^(2)],[omega,omega^(2),1],[omega^(2),1,omega]|

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

If omega=-(1)/(2)+i (sqrt(3))/(2) , the value of [[1, omega, omega^(2) ],[ omega, omega^(2), 1],[ omega^(2),1, omega]] is

Let omega be the complex number cos (2 pi)/(3)+i sin (2 pi)/(3) . Then the number of distinct complex number z satisfying [[z+1,omega,omega^(2)],[omega,z+omega^2,1],[omega^(2),1,z+omega]] = 0 is equal to

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

if omega be the cube root of unit then what is the value of |[1,omega ,omega^2],[omega, omega^2,1],[omega^2,1,omega ]| ?

(b) answer any one of the foll.: (i) prove without expanding |[1,omega,omega ^2],[omega ,omega ^2 ,1],[omega ^2,1, omega]|=0 wher w is an imaginary cube root of unity.

Using properties, prove that |[1,omega,omega^2],[omega,omega^2,1],[omega^2,1,omega]|=0 where omega is a complex cube root of unity.

Evaluate the following determinants. [[1,omega,omega^2],[omega,omega^2,1],[omega^2,1,omega]]

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

find determinant of |(1, omega, omega^(2)),(omega, omega^(2),1),(omega^(2),1,omega)|=