Bukhari

Hadith Commentary:
(1)
From this hadith, it is understood that in the previous hadith, what is meant by making dhikr aloud is saying "Allahu Akbar," that is, the Messenger of Allah (sallallahu alayhi wa sallam) would say "Allahu Akbar" aloud after concluding the obligatory prayer with salam. This establishes that the imam and the followers should, immediately upon finishing the prayer, say "Allahu Akbar" aloud once. The proof for reciting other supplications after completing the prayer is also found in the ahadith. Thus, it is narrated from Thawban (radi Allahu anhu) that when the Messenger of Allah (sallallahu alayhi wa sallam) finished his prayer, he would say "Astaghfirullah" three times and then say these words:
"Allahumma anta as-salam wa minka as-salam tabarakta ya dhal-jalali wal-ikram" — "O Allah! You are the embodiment of peace. From You is all peace. O Possessor of majesty and honor! You are supremely blessed."
(Sahih Muslim, al-Masajid, Hadith: 1334(591))

(2)
At the end of the hadith, there is mention of Abu Ma‘bad, the freed slave of Ibn Abbas (radi Allahu anhu), regarding whom the narrator of the hadith, Amr ibn Dinar, says that when I mentioned this hadith to Abu Ma‘bad, he plainly denied it, saying, "I did not narrate this hadith to you." Imam al-Shafi‘i (rahimahullah) has said that perhaps he forgot after narrating it; in any case, there is no doubt regarding the authenticity of the hadith.
(Fath al-Bari: 2/421)

Hadith Commentary:
Benefits and Issues:
Abu Ma‘bad later denied narrating this hadith, saying, “I did not narrate this report to you.” However, according to the hadith scholars, if a narrator denies his own narration but the person transmitting from him is reliable and trustworthy, then the narration is acceptable. For this reason, Imam Muslim rahimahullah included the narration despite the denial of transmission.

1336. Commentary:

➊ Remembrance (dhikr) after completing the prayer is Sunnah. It should begin with "Allahu Akbar." The voice should be moderate—neither too loud nor completely soft—so that when all the followers' voices join together, a kind of resonance is produced. The rest of the remembrance should be done quietly.

➋ Ibn Abbas (radi Allahu anhuma), due to being underage, used to stand in the back rows, so the sound of the salam would not reach him. After the salam, when the sound of the takbir would resonate, he would realize that the prayer had ended. It is possible that one wisdom behind saying the takbir in a loud voice is so that people know the prayer has ended, just as the transitional takbirs in prayer are said aloud, and the adhan is called aloud, etc. Therefore, the opinion that it is preferable to conceal the remembrance and that the takbir after the salam should be said quietly—as is the position of the majority of scholars—is weak.

Benefit:
It is established from this hadith that after concluding the prayer with salam, one should say "Allahu Akbar" aloud. However, nowadays some people have abandoned the Sunnah and adopted innovation, such that instead of saying "Allahu Akbar," they all together recite «لا اله الا الله» aloud after the salam, or they begin to chant "Allah Hu Allah Hu." These are absolutely un-Islamic practices. Saying "Allahu Akbar" aloud after the completion of the prayer is Sunnah. Shaykh Abu ‘Umar Abdul Aziz Nooristani (hafizahullah) has written a separate treatise on this issue, which is worthy of study. See [سلسلة مجموع الرسائل الشيخ نورستاني صفحہ : 400 تا 426]