It has been asked to prove that a grammar is unambiguous which seem ambiguous to me
You need to revisit the definition of ambiguity. The point is not whether multiple derivations exist; all non-linear grammars have many derivations per word.
You have to check if there is only one left-derivation per word. Equivalently, you can check right-derivations or syntax trees.

If you think this grammar is ambiguous, prove it by giving two different syntax trees for some word.

If you think it is unambiguous, see here for how to prove that; it's often more tricky.