Ambiguity has no relation with left most and right most derivation.It is true.Every grammer if it has some string then it will have both left and right deravation

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"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