If `omega` is a cube root of unity then `|(a,b,c),(b,c,a),(c,a,b)|` has a factor

If omega is an imaginary cube root of unity , prove that, |{:(a,b,c),(b,c,a),(c,a,b):}|=-(a+b+c)(a+bomega+comega^2)(a+bomega^2+comega)

If w is a complex cube root of unity. |(a,b,c),(b,c,a),(c,a,b)| = -(a +b +c) (a + bk + ck^(2)) (a + bk^(2) + ck) , then k equals

If a^3+b^3+6a b c=8c^3 & omega is a cube root of unity then: (a) a , b , c are in A.P. (b) a , b , c , are in H.P. (c) a+bomega-2comega^2=0 (d) a+bomega^2-2comega=0

If omega is a non real cube root of unity, then (a+b)(a+b omega)(a+b omega^2)=

If omega is a non real cube root of unity then (a+b)(a+b omega)(a+b omega^(2)) is

If omega is a non real cube root of unity, then (a+b)(a+b(omega))(a+b(omega)^2) is

If a^(3)+b^(3)+6abc=8c^(3)& omega is a cube root of unity then: a,b,c are in Adot P*( b) a,b,c, are in Hdot P*a+b omega-2c omega^(2)=0a+b omega^(2)-2c omega=0

If omega is a non-ral cube root of unity then the value of (a+b) (a+b omega) (a+b omega ^(2)) is-

If omega is a complex cube root of unity, then (a+b omega+c omega^(2))/(c+a omega+b omega^(2))+(c+a omega+b omega^(2))/(a +b omega+c omega^(2))+(b+c omega+a omega^(2))/(b+c omega+a omega^(5))=