Ruling on the prayer of one who wiped over socks while forgetting that he had put them on without ritual purity

Q: A question from: S. A. G. from Hail, who says: I performed wudu for Fajr and prayed, and I forgot to put on the socks (shoes). I slept after the prayer, then woke up to go to work and put on the socks without being in a state of ritual purity. When the time for Zuhr came, I performed wudu, wiped over the socks, and prayed. I did the same for Asr, Maghrib, and Isha, believing that I had put them on while in a state of ritual purity. I did not remember that I had not put them on while in a state of ritual purity until about two hours after Isha. What is the ruling on my prayers in these four times? Are they valid or not? I did not do this intentionally.

A: If one puts on khuffayn (leather socks) or socks—which are the shoes—without being in a state of ritual purity, and wipes over them and prays while forgetting, his prayer is invalid, and he must repeat all the prayers he performed with this wiping. This is because a condition for the validity of wiping over them is that they be put on while in a state of ritual purity, by the consensus of the scholars. One who puts them on without being in a state of ritual purity and wipes over them is in the same position as one who prays without being in a state of ritual purity. The Prophet (peace and blessings be upon him) said: This was narrated by Muslim in his Sahih from the hadith of Ibn Umar (may Allah be pleased with them both). And in the two Sahihs, from the hadith of Abu Hurayrah (may Allah be pleased with him) , the Prophet (peace and blessings be upon him) said: .
And in the two Sahihs, from al-Mughirah ibn Shu'bah (may Allah be pleased with him) , that he was with the Prophet (peace and blessings be upon him) on one of his journeys. He went to relieve himself, then returned and performed wudu, and al-Mughirah was pouring water over him. When the Prophet (peace and blessings be upon him) wiped his head, al-Mughirah reached out to remove his khuffayn, but the Prophet (peace and blessings be upon him) said: So he wiped over them. There are many hadiths on this topic.
By this, you, O questioner, should know that you must repeat the four prayers: Zuhr, Asr, Maghrib, and Isha. There is no sin on you because of the forgetfulness; for Allah the Exalted said: [al-Baqarah: 286]. And it is authentically narrated from the Prophet (peace and blessings be upon him) that he said: The meaning of this is that He (Glorified and Exalted is He) responded to the supplication of His servants by not holding them accountable for what occurred from them due to mistake or forgetfulness. Praise and thanks to Allah for that.