Addendum: An explanation of what came in the Sunnah regarding how the one who is praying returns the greeting.

The Shaykh : I do not wish to explain this hadith; rather, I return to the hadith of Ibn Mas'ud. When he greeted the Prophet (peace and blessings be upon him) and did not hear a verbal response to the greeting, he said: "What is near and what is far have taken hold of me", meaning he began to think about what he had done, near or far, wondering what he had committed or in what he had contradicted the Shari'ah such that the Messenger of Allah (peace and blessings be upon him and his family) did not return his greeting. Then the answer came after he (peace and blessings be upon him) had completed his prayer: , meaning in his religion, as he (peace and blessings be upon him) said in another hadith: . He (peace and blessings be upon him) said in the hadith of Ibn Mas'ud: . It is as if he is excusing Ibn Mas'ud, who was troubled by what was near and what was far. Do not be concerned, for a new ruling has been revealed, which is that there is no speech in prayer. Therefore, I did not return your greeting; I was content with a gesture. This gesture is the crux of this statement. This gesture is the sign and the alternative to returning the greeting verbally, which was prescribed previously. So, if someone greets the one who is praying, he has one of two states or one of two gestures by which he should return the greeting. If he is in a crowded place, like this blessed mosque which was full of worshippers, and the one entering says "Peace be upon you" without raising his voice much, but only greets those around him, then they should gesture with their hand. This gesture indicates that if the one entering is behind the rows, then the hand should be raised so that it is seen. Let not what confused Ibn Mas'ud confuse the Muslim, so that he wonders why they did not return his greeting. At least some of them should raise their hands, because returning the greeting is a collective obligation (fard kifayah); if some fulfill it, it is lifted from the rest. And if the Muslim is coming from the direction of the qiblah such that the worshippers see him and he sees them, then it is sufficient for the one returning the greeting to raise his hand like this, without rushing to raise it, to achieve the alternative to the verbal return of the greeting, which is "And upon you be peace." He has the choice between returning the greeting with a gesture of his hand or returning the greeting with a gesture of his head. This second gesture is only to be used if the gathering is small or if the worshipper is alone, in which case the return of this greeting is shown by this gentle and easy gesture.
This is the first type I wanted to draw attention to, regarding how the one who is praying returns the greeting to the one who greeted him. And before I move on to the second type, it is necessary to remind you here that offering the greeting, as we said in the previously mentioned hadith: . Therefore, the one entering the prayer place or the mosque who meets his brother or his Muslim brothers who are praying must greet them first because he has met them, but the return of the greeting is only by gesture, as we mentioned.