Narrated Abu Ma`bad: (the freed slave of Ibn `Abbas) Ibn `Abbas told me, "In the lifetime of the Prophet it was the custom to celebrate Allah's praises aloud after the compulsory congregational prayers." Ibn `Abbas further said, "When I heard the Dhikr, I would learn that the compulsory congregational prayer had ended."
Hadith Referenceصحيح البخاري / كتاب الأذان (صفة الصلوة) / 841
Hadith Gradingمحدثین:أحاديث صحيح البخاريّ كلّها صحيحة
And Ibn Abbas said: I used to know when they had finished (the prayer) by hearing that (remembrance). Ibn Abbas (radi Allahu anhu) said that by hearing the remembrance (dhikr), I would understand that the people had completed their prayer.
Source: Sahih Bukhari: Commentary by Maulana Dawood Raz, Page: 841
Shaykh Abdul Sattar al-Hammad
Hadith Commentary: In the hadith, the virtue of remembrance (dhikr) after the prayer is transmitted, but what is meant by this remembrance? In the present era, the collective and loud chanting of "Allah" after the prayer, as is commonly practiced, is absolutely an un-Islamic act. Rather, what is meant here is saying "Allahu Akbar," as will be clarified in the following hadith.
Source: Hidayat al-Qari: Commentary on Sahih Bukhari, Urdu, Page: 841
Ibn Abbas said: To raise the voice for making the mention of Allah after the people had finished their obligatory prayer was for in vogue the time of the Messenger of Allah ﷺ. Ibn Abbas said: I used to know by it when they finished the prayer and would listen to it (making the mention of Allah).
Shaykh Umar Farooq Saeedi
1003. Commentary: After the salam, saying «الله اكبر» and «استغرالله» three times, as well as some other phrases—especially in a raised voice—is an established Sunnah. It is not correct to interpret this as something to be done only occasionally or merely for the purpose of teaching. However, it is necessary that the raising of the voice should not be to such an extent that it causes disturbance or confusion for others.
Source: Sunan Abu Dawood – Commentary by Shaykh Umar Farooq Saeedi, Page: 1003