Let grammar is like this :
$S \rightarrow a$
$A \rightarrow AbA$
This grammar is left as well as right recursive but still unambiguous.. A is useless production but still part of grammar..
A grammar having both left as well as right recursion may or may not be ambiguous ..
Let's take a grammar say
$S\rightarrow SS$
Now, according to the link https://en.wikipedia.org/wiki/Formal_grammar
For a grammar G, if we have L(G) then all the strings/sentences in this language can be produced after some finite number of steps .
But, for the grammar $$S\rightarrow SS$$
Can we produce any string after a finite number of steps ? NO, and hence language of this grammar is empty set {} .
Hence, If a grammar is having both left and right recursion, then grammar may or may not be ambiguous .