Can you please tell me if this is a correct solution to this problem.

Q) Give an example of a non-regular language A {0, 1}* for which Prefix(A) is regular. Answer) Take a classic example of non-regular language such that A={0ⁿ1ⁿ, n >= 0}. We can prove why this is non-regular by pumping lemma. But the prefix of A is of form {0*1*} which can easily be proven to be regular by creating a simple DFA.