Here is the Reference from the al Muwatta about the 3 Tasleemat:
Yahya related to me from Malik from Nafi that Abdullah ibn Umar used
to say the tashahhud saying, "In the name of Allah. Greetings belong
to Allah. Prayers belong to Allah. Pure actions belong to Allah. Peace
be on the Prophet and the mercy of Allah and His blessings. Peace be
on us and on the slaves of Allah who are salihun. I testify that there
is no god except Allah. I testify that Muhammad is the Messenger of
He used to say this after the first two rakas and he would make
supplication with whatever seemed fit to him when the tashahhud was
completed. When he sat at the end of the prayer, he did the tashahhud
in a similar manner, except that after the tashahhud he made
supplication with whatever seemed fit to him. When he had completed
the tashahhud and intended to say the taslim, he said, "Peace be on
the Prophet and His mercy and blessings. Peace be upon us and on the
slaves of Allah who are salihun."
He then said, "Peace be upon you" to his right, and would return the
greeting to the imam, and if anyone said "Peace be upon you" from his
left he would return the greeting to him.
Note that a big minority of scholars, say that the taslim is as follows: saying as-salamu 'alaikum on the right, wa 'alaikum as-salam to the Imam and as-salamu 'alaikum to a person on the left. The majority doesn't say that in all three taslmeet you use the same wording: as-salamu 'alaikum. But most say that the tasleem towards the Imam is only said in the heart (not pronounced). Also note this narration is a clear evidence against the saying of ibn 'Arabi that the 3rd taslimah is a bid'ah, as if it was so how come a sahabi like ibn 'Omar who was known even to pray to rak'a in a place only because he saw our Messenger (peace be upon him) doing it there, following the guidance of our Prophet, would do something which we may call bid'ah?
And one of two hadiths mentioned on the 1 Tasleem in the Riwaya of Yahya ibn Yahya Al-Laithy of the Muwatta'
Yahya related to me from Malik from Yahya ibn Said al-Ansari that
al-Qasim ibn Muhammad ibn Muhammad told him that A'isha, the wife of
the prophet, may Allah bless him and grant him peace, used to say in
"Greetings, good words, prayers, pure actions belong to Allah. I
testify that there is no god except Allah, alone without partner, and
I testify that Muhammad is the slave of Allah and His Messenger. Peace
be upon you, Prophet, and the mercy of Allah and His blessings. Peace
be upon us and on the slaves of Allah who are salihun . Peace be upon
you . "
Note that ibn Majah, at-Tirmdihi, abu Dawod, al-Hakim, at-Tabari, a-Daraqotni, ibn Khozaymah and also Imam Ahmad have quoted similar ahadith as the one quoted by Tamer Shlash. This apparently was how people in Medina used to do tasleem, while in 'iraq it was used to perform two tasleemat saying: as-salmu 'laikum wa rahmatu-Llah to the right and left.
The one taslimah is not only reported on the authority of 'Aisha, but also by Sahl ibn Sa'id, ibn 'Omar ("كَانَ رَسُولُ اللَّهِ صلى الله عليه وسلم يَفْصِلُ بَيْنَ الشَّفْعِ وَالْوِتْرِ بِتَسْلِيمَةٍ يُسْمِعُنَاهَا" in Musnad Ahmad 2/76 and sahih ibn Hebban 6/191) and Salamah ibn al-Awka' and from the doing of the muhajireen among the sahaba according ibn al-Mundhir (see for example in Sunan ad-Daraqutni, Musanaf ibn Shabyah -who quoted that Abu Bakr, 'Omar, Anas, al-Hassan (al-Basri),... -he counted 16 sahabi and tabi'i- used to do so in Musanaf abd-Araazaq and at-Tabari even 'Othman has been added to the list and in a Quote of al-Hassan even our Messenger (peace be upon him)).
وقال ابن المنذر : قال عمار بن أبى عمار : كان مسجد المهاجرين يسلمون تسليمة واحدة ، وكان مسجد الأنصار يسلمون تسليمتين
In the Maliki Madhab it is sufficient to say in the Tasleem "As-salamu alaykum", but for example if the Imam says only "salamu alaykum" this is a wrong Tasleem, this means only with the correctly pronounced words you end the prayer!
Muwatta al Imam Malik is considered as one of the highest Sahih Books. Imam Shafi-i said that it is the most authentic book after the Quran" (at that time the Sahih Books of Bukhari and Muslim didn't exist)
Read also this fatwa, according to this fatwa in Arabic the Muhajiroon used to perform one taslimah.