If `omega` is a complex cube root of unity, show that
`[[1 , omega, omega^2], [ omega, omega^2, 1],[ omega^2, 1, omega]] [[1],[ omega],[ omega^2]]=[[0],[ 0],[ 0]]`

If omega is an imaginary cube root of unity, then (1 + omega - omega^(2))^(7) is equal to

If omega is a cube root of unity, then find (3+5omega+3omega^(2))^(2)+ (3 +3omega+5omega^(2))^(2)

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.

Let omega ne 1 be cube root of unity and (1 + omega ) ^(7)= a + omega. Then the value of a is

If omega be the complex cube root of unity and matrix H=[(omega,0),(0,omega)] , then H^(70) is equal to a)0 b)-H c)H d) H^(2)

IF 1, omega , omega^2 are the cube roots of unity and if [{:(1+omega,2 omega),(-2 omega,-b):}]+[{:(a,-omega),(3 omega,2):}]=[{:(0, omega),(omega,1):}] then a^2+b^2 is equal to

If omega is a complex cube root of unity, then value of Delta=|(a_(1)+b_(1)omega,a_(1)omega^(2)+b_(1),c_(1)+b_(1)omega),(a_(2)+b_(2)omega,a_(2)omega^(2)+b_(2),c_(2)+b_(2)omega),(a_(3)+b_(3)omega,a_(3)omega^(2)+b_(3),c_(3)+b_(3)omega)| is a)0 b)-1 c)2 d)None of these

Without expanding at any stage, prove that the value of the following determinant is zero. |(1,omega,omega^(2)),(omega,omega^(2),1),(omega^(2),1,omega)| , where omega is cube root of unity