"An unambiguous grammar has same leftmost and rightmost derivation"
This statement is false, let me take an example, suppose given gammer is (which is certainly unambiguous)
S -> AB A -> a B -> b
Suppose our input string is ab
Left Most Derivation S -> AB -> aB -> ab
Right Most Derivation S -> AB -> Ab -> ab
Notice Left Most derivation and Right most derivation are not same, still gammer is unambiguous.
Here is the Derivation Tree