It is narrated from Abdur Rahman bin Uthman Taimi that Sayyiduna Umar bin Khattab, may Allah be pleased with him, used to say: Wash your private parts with water.
Yahya said: Imam Malik, may Allah have mercy on him, was asked about a person who performed ablution and, out of forgetfulness, washed his face before rinsing his mouth, or washed his hands before washing his face. Imam Malik, may Allah have mercy on him, said: Whoever washed his face before rinsing his mouth should rinse his mouth and not wash his face again. But whoever washed his hands before washing his face should wash his face and then wash his hands again, so that the washing of the hands comes after the washing of the face, as long as the one performing ablution is still in his place or near it.
Yahya said: Imam Malik, may Allah have mercy on him, was asked about a person who forgot to rinse his mouth or put water in his nose during ablution and then performed the prayer. Imam Malik, may Allah have mercy on him, said: His prayer is valid; it is not necessary for him to repeat the prayer, but for the next prayer he should rinse his mouth or put water in his nose.
Hadith Referenceموطا امام مالك رواية يحييٰ / كتاب الطهارة / 35
........ Among the Hanafis, Malikis, and Shafi'is, this is the prevailing fatwa, because they do not count rinsing the mouth (kuli) and cleaning the nose (istinshaq) among the obligations (wajibat). However, the continuous practice of the Messenger of Allah (sallallahu alayhi wa sallam) and his command to rinse the mouth and clean the nose is evidence of their being obligatory.
[ابو داود: 142، 144، اس كي سند صحيح هے]
For this reason, Imam Ahmad (rahimahullah), Ishaq ibn Rahwayh (rahimahullah), Shawkani (rahimahullah), Albani (rahimahullah), and Siddiq Hasan Khan (rahimahullah), among others, hold this view. And it is clear that when this is obligatory, then without them neither ablution (wudu) nor prayer (salah) will be valid. «والله اعلم بالصواب»
Source: Muwatta Imam Malik by Abu Samia Mahmood Tabassum, Page: 35