If ab #0 then the points have to be in one of the quadrant and not on origin or any axis line.
now (-a,b) and (-b,a) will be in same quadrant only when a=b.
So points are (-a,a) or (-b,b) so one of them will be of poosite sign. as we don't know about if a > or a<0 so two posibilities:
2nd or 4th quadrant.
Now let us check the choices :
A) XY>0 this means both positive or both negative. so no chance it would be in same quadrant(2nd or 4th). SO we can answer no. Hence A is sufficient.
B) AX>0 this does not give any info of Y and A is new variable. So not siffiient.
Answer should be A.
Please confirm or correct.
Regards
Kripa