How to find whether a grammar is ambiguous? $$S\rightarrow aAB$$
$$A\rightarrow bBb$$
$$B\rightarrow A|\epsilon$$

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.
Since you are trying to prove that the grammar is ambiguous, you must simply provide an example of a string where that grammar results in more than one parse tree or derivation. (Note that this is an entirely different ordeal than trying to prove that a grammar is unambiguous.) Since the string abbbb indeed has two distinct leftmost  derivations, you have shown that the grammar is ambiguous. This proves that the grammar is not unambiguous since it is not the case that each string has at most one parse tree or derivation.