Imam offers Salah without Wudu'

Q 1: After I offered Salah (Prayer) in congregation, I remembered that I had not performed Wudu' (ablution). Should I perform Wudu' and repeat the Salah? (Part No. 5; Page No. 147

A: Wudu' is one of the preconditions of Salah, because Allah has commanded us to perform it before Salah. Allah (Exalted be He) says: O you who believe! When you intend to offer As-Salât (the prayer), wash your faces and your hands (forearms) up to the elbows, rub (by passing wet hands over) your heads, and (wash) your feet up to ankles. It was authentically reported that the Prophet (peace be upon him) said: Allah does not accept Salah from anyone if they invalidate their Wudu' until they perform Wudu' again. (Related by Ahmad, Al-Bukhari, Muslim, Abu Dawud, and Al-Tirmidhy) Therefore, the Salah that you offered forgetfully without performing Wudu' is invalid, since it lacks one of the preconditions of Salah; and you have to repeat it after performing Wudu'. You are free from blame for offering Salah without Wudu', for you are legally excused due to forgetfulness.May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.