If `|{:(p,-q,0),(0,p,q),(q,0,p):}|=0`, then which one of the following is correct ?

Options

A. p is one of the cube roots of unity
B. q is one of the cube roots of unity
C. `(p)/(q)` is one of the cube roots of unity
D. None of the above

Answer

C

Explanation

Let `|{:(p,-q,0),(0,p,q),(q,0,p):}|=0`
`rArr p(p^(2))+q(-q^(2))+0=0`
`rArr p^(3)-q^(3)=0`
`rArr p^(3)=q^(3)`
`rArr (p^(3))/(q^(3))=1 rArr ((p)/(q))^(3)=1`
`rArr (p)/(q)` is one of the cube roots of unity.