Commutativity preserving linear maps on central simple algebras

Let F be a field with char(F)=0, and let A be a finite dimensional central simple algebra over F with dimFA≠4. If a linear map satisfies (x2) (x)= (x) (x2) for all x A (in particular, if preserves commutativity), then is either a standard commutativity preserving map or its range is commutative.