Find the value of `k` if `|[1,1,1],[1,-omega^2-1,omega^2],[1,omega^2,omega^7]|=3k`

find the value of |[1,1,1],[1,omega^(2),omega],[1,omega,omega^(2)]| where omega is a cube root of unity

Let omega=-(1)/(2)+i(sqrt(3))/(2), then value of the determinant [[1,1,11,-1,-omega^(2)omega^(2),omega^(2),omega]] is (a) 3 omega(b)3 omega(omega-1)3 omega^(2)(d)3 omega(1-omega)

The value of det[[1,1,11,omega,omega^(2)1,omega^(2),omega]]

Let omega be a complex number such that 2omega+1=z where z=sqrt(-3) . If |{:(1,1,1),(1,-omega^(2)-1,omega^(2)),(1,omega^(2),omega^(7))|=3k , then k is equal to

Let omega = - (1)/(2) + i (sqrt3)/(2) , then the value of the determinant |(1,1,1),(1,-1- omega^(2),omega^(2)),(1,omega^(2),omega^(4))| , is

Let omega=-(1)/(2)+i(sqrt(3))/(2). Then the value of the determinant det[[1,1,11,1,omega^(2)1,omega^(2),omega^(4)]]3 omega(omega-1)(C)3 omega^(2)(D)3 omega(1-omega)

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

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)|.