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

Options

A. 1
B. `-z`
C. z
D. -1

Answer

2

Explanation

Here `omega ` is complex cube root of unity
Applying `R_(1) to R_(1)+R_(2)+R_(3),` the given matrix reduces to
` |{:(3,,0,,0),(1,,-omega^(2)-1,,omega^(2)),(1,,omega^(2),,omega):}|= 3(-1-omega -omega) = -3z`
`rArr k=-z`