$S\underset{1}{ \rightarrow} aS$
$\quad \underset{2}{\rightarrow} aA$
$ \quad \underset{3}{\rightarrow} aaAb$
$\quad \underset{4}{ \rightarrow} aabAab$
$\quad \underset{5}{ \rightarrow} aabbAaab$
$\quad \underset{6}{ \rightarrow} aabbaab$
Thus $6$ steps are needed and only one way to derive the string so only one parse tree.
Correct Answer: $A$