Pumping lemma for $a^n b^{2n}$

Question

I have this question and i am not sure and trying to solve in both way that is through diagram and expression:

Question : Prove that $a^nb^{2n}$ is not regular.

contradiction:

 Assume language is regular
----->()------>()------>(o)
      x         y        z

     x y^i z

 through diagram:  abb    when y^0
                   aabb      , y^1
                   aaabbb       y=2
so given language is not regular.

Is it correct?? Thanks