Abstract
In the present paper, our aim is to prove the following result: let R be a prime ring of a characteristic different from two. If Delta(1), Delta(2) are two symmetric generalized biderivations on R with associated biderivation D such that [Delta(1) (x, x), Delta(2)(x, x)] = 0 for all x is an element of R, then the following results hold:
1. R is commutative.
2. Delta(1) and Delta(2) act as left bi-multipliers on R.