(2-omega)(2-omega^(2))(2-omega^(10))(2-o...

`(2-omega)(2-omega^(2))(2-omega^(10))(2-omega^(11))="…….."`, where `omega` is the complex cube root of unity

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Prove that the value of determinant |{:(1,,omega,,omega^(2)),(omega ,,omega^(2),,1),( omega^(2),, 1,,omega):}|=0 where omega is complex cube root of unity .

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If z=omega,omega^2w h e r eomega is a non-real complex cube root of unity, are two vertices of an equilateral triangle in the Argand plane, then the third vertex z may be represented by (a) z=1 b. z=0 c. z=-2 d. z=-1

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Let omega!=1 be cube root of unity and S be the set of all non-singular matrices of the form [(1,a, b), (omega, 1, c), (omega^2, omega, 1)] , where each of a ,b and c is either omegaoromega^2 Then the number of distinct matrices in the set S is a. 2 b. 6 c. 4 d. 8

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