If a baseball pitcher were equally talented pitching left or right handed can he switch in the middle of an at bat?

pitchers may not switch throwing hands in the middle of an at bat. they may switch from hitter to hitter however There is nothing I have found in the MLB rules that states a pitcher cannot switch throwing hands when facing a single batter. Maybe someone can point out the specific rule that states what the above answerer says is factual? There is no rule in the official baseball scores that say a pitcher cannot change his hands. However, just as a batter cannot switch while the pitcher is on the rubber, so too can the pitcher not switch while on the rubber, as that would be an illegal motion while in the set position and be considered a balk (with runners on) or a ball (with bases empty).