Prove `|[1,omega,omega^(2)],[omega,omega^(2),1],[omega^(2),1,omega]|=0,` where`omega=-(1)/(2)+(i sqrt(3))/(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]] =

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

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

Prove that (1-omega-omega^(2))(1-omega+omega^(2))(1+omega-omega^(2))=8

Show that det ([1,omega,omega^(2)omega,omega^(2),1omega,omega^(2),1omega^(2),1,omega])=0 where omega is the non-real cube root of unity =0 where omega is

Evaluate |(1,omega,omega^2),(omega,omega^2,1),(omega^2,omega,omega)| where omega is cube root of unity.

{[(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))]

Which of the following is a non singular matrix? (A) [(1,a,b+c),(1,b,c+a),(1,c,a+b)] (B) [(1,omega, omega^2),(omega, omega^2,1),(omega^2,1,omega)] where omega is non real and omega^2=1 (C) [(1^2,2^2,3^2),(2^2,3^2,4^2),(3^2,4^2,5^2)] (D) [(0,2,-3),(-2,0,5),(3,-5,0)]