If a worshipper adds a rak'ah to the prayer out of forgetfulness and remembers this during the prayer or after it, does he prostrate for forgetfulness? Or is his prayer invalid?

The questioner : If you permit me one last question.

The Shaykh: Yes.

The questioner : If a person adds a rak'ah to one of the prayers?

The Shaykh : Ah

The questioner : So if he realizes it during the extra rak'ah or after the completion of the prayer, does he have to prostrate for forgetfulness, or is his prayer invalid, or does he owe nothing?

The Shaykh : Yes, he has to prostrate the prostration for forgetfulness, and that is to compensate for the addition that occurred. This is supported by two hadiths, one of which is well known in the two Sahihs and is known among the scholars as the hadith of Dhu al-Yadayn. The Prophet (peace and blessings be upon him) prayed the 'Asr prayer with two rak'ahs, then he moved to a side of the mosque, lay down, and placed one leg over the other. Among the people were Abu Bakr and the senior Companions, and no one spoke except Dhu al-Yadayn, who said: "O Messenger of Allah, was the prayer shortened or did you forget?" He (peace be upon him) said: "None of that happened." He said: "Yes, it did happen, O Messenger of Allah." So he looked at the faces of his Companions and said: "Is Dhu al-Yadayn telling the truth?" They said: "Yes." So he stood up to his place, and I do not say to his mihrab, because there was no mihrab in his mosque (peace be upon him), and he prayed the two forgotten rak'ahs, then he prostrated the two prostrations of forgetfulness.
The Shaykh : The other incident, which is more important, is that he (peace be upon him) prayed the Maghrib prayer with two rak'ahs and said the taslim. Just as some people did in the first prayer, here the people left quickly. So it was said to him: "Did you pray two rak'ahs?" So he ordered the iqamah to be called, and the iqamah was called to indicate to those who had left quickly that he was in prayer, so they returned. He came and completed the rak'ah and prostrated the two prostrations of forgetfulness.
The Shaykh : So this means that when the worshipper remembers his mistake, he either makes up for it if it was a deficiency, for example, or there is no way to make up for it because it was an addition, so he prostrates the two prostrations of forgetfulness, and these two prostrations compensate for the addition or deficiency that occurred from him, even if there was this interval, because this interval was not in vain and was not for play.