Is a*b* regular?

Question

I know aⁿbⁿ for n > 0 is not regular by the pumping lemma but I would imagine a*b* to be regular since both a,b don\'t have to be the same

Answer 1

To prove that a language is regular, it is sufficient to show either:

1) There exists some DFA that recognizes it. In this case, the DFA is trivial.

2) The language can be expressed as a regular expression, as mentioned in another answer. a*b* is a regular expression to recognize this language.