Is L = {a^n a^n b^m |m, n ≥ 0} a regular or irregular language?

Question

I have troubles in solving/proving this problem. I can understand that in a non regular no Finite State Automaton/Machine can be written that validates and accepts this input since it lacks a memory component. (Please correct me if I'm wrong)

The wikipedia entry on Regular Language also lists this example, but does not provide a (mathematical) proof why it is not regular.

Answer 1

This language is accepted by the regular expression (aa)*b*, so yes, it is a regular language.

Answer 2

We can construct a deterministic finate automta for the given language L={a^n a^n b^m | m,n>=0} . So the given language is regular