Bukhari

Hadith Commentary:

In another narration, it is mentioned that Umar ibn Abd al-Aziz rahimahullah asked Sayyid ibn Yazid radi Allahu anhu about assistance.

Sayyid ibn Yazid radi Allahu anhu was with the Messenger of Allah sallallahu alayhi wa sallam’s belongings during the Farewell Pilgrimage (Hajjat al-Wada‘), and at that time he had reached puberty.

From this, it is also established that children performing Hajj is proven.

Hadith Commentary:
(1)
It is permissible and valid for a child to perform Hajj.
There is no difference of opinion on this issue.
It is mentioned in Sahih Muslim that a woman lifted up her child and asked the Messenger of Allah (sallallahu alayhi wa sallam):
Is the Hajj of this child valid? He replied:
“Yes, and you will have the reward for it.”
(Sahih Muslim, Al-Hajj, Hadith: 3254(1336))
From this, it is understood that the Hajj of a child is legislated (mashru‘), but this Hajj does not fulfill the obligation (fard) of Hajj; rather, after reaching puberty, the child will have to perform the obligatory Hajj again, because a child is not held accountable (marfu‘ al-qalam) until reaching puberty, therefore Hajj is not obligatory upon him.
If a child invalidates his Hajj, then making it up (qada) is not necessary for him, nor is any expiation (fidya) obligatory upon him.
(2)
Imam Bukhari (rahimahullah) has established his chosen heading by citing the Hajj performed by Abdullah ibn Abbas (radi Allahu anhuma) and Sa’ib ibn Yazid (radi Allahu anhu), because both of these individuals were minors at the time of Hajj, yet they performed Hajj in the company of the Messenger of Allah (sallallahu alayhi wa sallam).
And this is the intended point.