I have a homework assignment:

Given following grammar

$
S \rightarrow A1B \\
A \rightarrow 0A \;|\; \varepsilon \\
B \rightarrow 0B \;|\; 1B \;|\; \varepsilon \\
$

* Show that this grammar is unambiguous.

* Find a grammar for the same language that is ambiguous, and demonstrate it.

I know if I was asked to prove that the language is ambigious then I should find two different parse trees for same string. But I don't know what to do for this question.