During prayer if a mistake is made in Qur'an reading, and I remember this in another stage or at the end of the prayer, does this affect the prayer?
All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Any person who involuntarily makes a mistake while reciting the Quran in the Prayer is excused and his Prayer is valid, and he is not supposed to do any additional act. The evidence for this is the Hadeeth narrated by Al-Miswar ibn Yazeed Al-Maaliki who said: “The Prophet prayed and left a verse. A man said to him: "O! Messenger of Allah the verse such and such. The Prophet said to him: ‘Why didn't you remind me of it’, (while praying).” [Abu Daawood and Ibn Hibbaan]
Ibn ‘Umar narrated that the Prophet performed a Prayer and got confused while reading a verse. When he left, he met Ubay and said to him: “Did you pray with us?” “Yes”, said Ubay.
Then the Prophet said to him: “So why didn't you (remind me of it (the verse).”
So, these two Ahadeeth are enough evidence that whoever was mistaken while reciting a verse of the Quran other than the al-Faatihah, his Prayer is valid, and he is not asked to perform any additional act. But if the mistake is in the al-Faatihah and if it changes the meaning, or he leaves out a letter of the al-Faatihah and he realizes that while praying, then he has to consider that Rak’ah (where the al-Faatihah was not recited properly) invalid and pray another Rak’ah for it.
On the other hand, if somebody remembers after finishing the Prayer and leaving the place where he prayed that he did not recite the al-Faatihah properly, then he has to pray that Prayer again as the first Prayer is invalid.
Allah knows best.
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