weird question

Question

Find all pairs of a and b such that the point (a, b) in rectangular coordinates is the same as (b, a) in polar coordinates.

Answer 1

(0,0) in rectangular coordinates is the origin,

(0,0) in polar coordinates is the origin, an angle of 0 degrees or 0 radians, with magnitude r= 0

switch a=0 and b=0 (a,b) to (b,a) and you get (0,0)