|[1,w^(3),w^(2)],[w^(3),1,w],[omega^(2),w,1]|

Prove that |[1,w^2,w^2],[w^2,1,w],[w^2,w,1]|=-3w where w is a cube root of unity.

Let omega=-(1)/(2)+i (sqrt(3))/(2) , then the value of |[1,1,1],[1,-1-omega^(2),omega^(2)],[1,omega^(2),omega^(4)]| is

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

If w is a complex cube root of unity, show that ([[1,w,w^2],[w,w^2,1],[w^2,1,w]]+[[w,w^2,1],[w^2,1,w],[w,w^2,1]])*[[1],[w],[w^2]]=[[0],[0],[0]]

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

Let triangle=|(1,1,1),(1,-1-w^(2),w^(2)),(1,w,w^(4))| where W ne 1 is a complex number such that w^(3)=1 then triangle equals

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

Given omega = -frac{1}{2}+frac{isqrt(3)}{2} , then the value of /_\=|[1,1,1],[1,-1-omega^(2),omega^(2)],[1,omega^2,omega^4]|

{[(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))]

Prove that , {[{:(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)):}]=[{:(0),(0),(0):}] where omega is the cube root of unit.