Since given grammar can have more than 1 parse trees for string '(())', so grammar is ambiguous,
and also A → AA has left recursion.
For predictive-parsing, i.e. LL(1), grammar should be:
- Free from ambiguity
- Free from left recursion
- Free from left factoring(Non Determinism)
Given grammar contains both ambiguity and left recursion, so it can not have a predictive parser. .We can remove left recursion easily but ambiguity of CFL is not easy to remove.(as it is undecidable)
option A is more appropriate.