Simplify `(omega^2+omega-1)^3-(omega^2-omega+1)^3`

The value of (1+omega^(2)+2 omega)^(3n)-(1+omega+2 omega^(2))^(3n) is

If omega be a complex cube root of unity,then the number (1-omega-omega^(2))^(3)+(omega-1-omega^(2))^(3)+(omega^(2)-omega-1)^(3) is: a.Divisible by 3 but not by 8 b.Divisible by 8 but not by 3 c.Divisible by both 3 & 8 d.none of these

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

If omega is cube root of unit, then find the value of determinant |(1,omega^3,omega^2), (omega^3,1,omega), (omega^2,omega,1)|.

If omega is a cube root of unity, prove that (1+omega-omega^2)^3-(1-omega+omega^2)^3=0

If 1,omega,omega^(2) are the roots of unity then (1-omega+omega^(2))^(3)+(1+omega-omega^(2))^3=

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)]