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If omega ne 1 is a cubit root unity and ...

If `omega ne` 1 is a cubit root unity and `|(1,1,1),(1,-omega^(2)-1,omega^(2)),(1,omega^(2),omega^(7))|` = 3 k, then k is equal to

A

1

B

`z`

C

`-z`

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
B
Here, `omega` is complex cube root of untiy.
Applying `R_(1) to R_(1) + R_(2) + R_(3)`, then 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`
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