Should someone who made a mistake and bowed before the Imam prostrate for forgetfulness alone after the prayer has ended?

The Imam bears responsibility for any inadvertent error (sahw) committed by the congregant (ma'mum) as long as the latter is following him, except for the omission of a complete rak'ah, a prostration (sajdah), the opening takbir (takbirat al-ihram), or the salutation (taslim). It is obligatory for the congregant not to precede the Imam in bowing (ruku') or other actions.