Hadith on Peace: The Prophet would end his prayers with invocations for peace and mercy

Alqama ibn Wa’il reported that his father said: I prayed with the Prophet, peace be upon him, and he would invoke peace on his right said, saying, “Peace, mercy, and blessings of Allah be upon you,” and again to his left side, saying, “Peace, mercy, and blessings of Allah be upon you.”

[Sunan Abu Dawud, Book of Prayer, Number 997, Hasan]

عَنْ عَلْقَمَةَ بْنِ وَائِلٍ عَنْ أَبِيهِ قَالَ صَلَّيْتُ مَعَ النَّبِيِّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ فَكَانَ يُسَلِّمُ عَنْ يَمِينِهِ السَّلَامُ عَلَيْكُمْ وَرَحْمَةُ اللَّهِ وَبَرَكَاتُهُ وَعَنْ شِمَالِهِ السَّلَامُ عَلَيْكُمْ وَرَحْمَةُ اللَّهِ

سنن أبي داود كِتَاب الصَّلَاةِ بَاب تَفْرِيعِ أَبْوَابِ الرُّكُوعِ وَالسُّجُودِ ووَضْعِ الْيَدَيْنِ عَلَى الرُّكْبَتَيْنِ – يسلم عن يمينه السلام عليكم ورحمة الله وبركاته وعن شماله السلام عليكم ورحمة الله