The given grammar is ambiguous.Let us see how.
First of all it is not left recursive since for left recursion we must have production of type
S --> Sa directly or indirectly which is not the case here.
Consider drawing the derivation of a string say ab , so ambiguity comes as which of the 2 "A's" to be substituted first.Either of them can be done.To elaborate , we see reduction of "ab" in 2 ways , sufficient to show grammar is ambiguous.
S --> Aab --> ab [In case second A is substituted by epsilon]
S --> aAb --> ab [In case first A is substituted by epsilon]
So corresponding to these 2 reductions , we will get different derivation trees.Hence the grammar is ambiguous.
For more reference and clarity , u can check the following link where
S -> aS | aSbS | epsilon is proved ambiguous on the similar ground :
https://cs.nyu.edu/courses/spring01/G22.2110-001/ans1.html
Hence A) should be the correct option.