|" 1a."|[1,omega,omega^(2)],[0,omega^(2),1],[omega^(2),1,omega]|=0," GEI "

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

If omega is complex cube root of 1 then S.T [(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

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.

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

Without expanding at any stage, prove that |{:(1,omega,omega^(2)),(omega,omega^(2),1),(omega^(2),1,omega):}| = 0

(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.

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