1. The problem statement, all variables and given/known data I'm reading Zee's book Einstein Gravity, I'm in the section where he said that given an array of two numbers p=(ap1, bp2), it is not a vector unless a=b. He just stated it without really showing how it must be like that. I know that a vector should satisfy a transformation p'=R(θ)p with R as the rotation matrix. In the exercises he also asked to prove that (p2q3, p3q1, p1q2) is not a vector by checking how it transforms under rotation. 2. Relevant equations p'=R(θ)p with R as the rotation matrix 3. The attempt at a solution For the first part, p'=Rp yields (ap1cosθ - bp2sinθ, ap1sinθ + bp2cosθ). I'm not sure what this is implying.