$$S\rightarrow aAB$$ $$A\rightarrow bBb$$ $$B\rightarrow A|\epsilon$$
I'm choosing the string abbbb.
First left most derivation is the following:
$$S\Rightarrow aAB\Rightarrow abBbB\Rightarrow abebB\Rightarrow abebA\Rightarrow abebbBb\Rightarrow abebbeb = abbbb$$
Second left most derivation is the following:
$$S\Rightarrow aAB\Rightarrow abBbB\Rightarrow abAbB\Rightarrow abbBbbB\Rightarrow abbebbB\Rightarrow abbebbe = abbbb$$
Can someone tell me whether I'm correct in saying that the grammar is ambiguous?
This question has been taken from chapter 5 of "An Introduction to Formal Languages and Automata" by Peter Linz 5th Edition. The question states to prove that the grammar is unambiguous (however it is not). Hence, the aim of posting this question is to make sure that I've understood ambiguity and distinction between parse trees properly. I'm studying formal languages on my own and do not have the luxury of an instructor.