An imam who realized he was not in a state of wudu' completed the prayer

The questioner:
Honorable Shaykh, may Allah grant you success. I am the imam of a mosque. I entered one of the prayers without wudu', having forgotten it, and I did not remember until the second rak'ah. It was a prayer recited aloud, so I completed the prayer because I knew that those behind me would not step forward to lead the prayer if I were to appoint one of them.

The Shaykh:
Yes.

The questioner:
If I did this and completed the prayer to avoid causing disturbance to the worshippers, is my action valid?

The Shaykh:
This prayer is invalid. The invalid one does not complete the prayer while you are not in a state of purity. However, if you appointed one of the ma'mum (those praying behind the imam) and he completed the prayer, there is no harm according to a group of scholars. If you appointed one and he prayed and completed the prayer, the people's prayer is valid according to the stronger opinion of the scholars. But if you concealed it and you were not in a state of purity, your prayer is invalid. You must repeat it. Their prayer is also invalid because the prayer of the ma'mum is invalidated by the invalidity of the imam's prayer. You made a mistake in this. Yes.