Allah Says in the Holy Quran Chapter 4 Surah
Nisaa verse 86:
86 When a (courteous) greeting is offered you meet it with a greeting
still more courteous, or (at least) of equal courtesy. Allah takes careful account of all things.
Sahih Al-Bukhari Hadith 1.27 Narrated by Abdullah bin Amr
A person asked Allah's Messenger (peace be upon him)
"What (sort of) deeds in or (what qualities of) Islam are good?" He (peace be upon him) replied, "To feed (the poor),
and greet (with Salaam) those whom you know and those whom you don't
know."
Al-Tirmidhi Hadith 849 Narrated by Abu Yusuf Abdullah ibn Salam
Abdullah heard the Prophet (peace be upon him) say: ‘O
people! Spread the Salaams
(greetings), feed (the poor and needy), behave kindly to your blood
relations, offer prayer when others are asleep, and (thus) enter Paradise in peace.
Shaking the hands of one another
Al-Tirmidhi Hadith 888 Narrated by Anas ibn Malik
A man asked the Prophet (peace be upon him): ‘O Messenger
of Allah (peace be upon him)! When any one of us meets a Muslim brother or a friend, should
he then bow his head (as a sign of courtesy to him)?’ He (peace be upon him) said: ‘No.’ The man said: ‘Should
he embrace and kiss him?’ He (peace be upon him)
said: ‘No.’ The man then asked: ‘Should
he clasp his hands?’ He (peace be upon him) said:
‘Yes.’
Al-Tirmidhi Hadith 4679 Narrated by Al-Bara' ibn Azib
The Prophet (peace be upon him) said: "Two Muslims
will not meet and shake hands without having their sins forgiven them before
they separate.
Sahih Al-Bukhari Hadith 8.279 Narrated by Qatada
I asked Anas bin Maalik (who served the
Prophet (peace be upon him) in his (peace be upon him) house for ten years), "Was it a custom of the
companions of the Prophet (peace be upon him) to shake hands with one another?" He said, "Yes."
Al-Tirmidhi Hadith 4681 Narrated by Abu Umamah
Allah's Messenger (peace be upon him) said, "The
perfect way for one of you to visit an invalid is for you to put your hand on
his forehead or on his hand and ask him how he is; and the perfect way for you
to greet one another is to shake hands."
Greeting one another with ‘Salaams’ and supplications, and
the shaking of hands when greeting, regardless if one uses only the right hand
or one wishes to clasp both hands, would be in accordance with the preferred
Sunnah of the Messenger of Allah (peace be upon him).
Whatever written of Truth and benefit is only
due to Allah’s Assistance and Guidance, and whatever of error is of me
alone. Allah Alone Knows Best and He is
the Only Source of Strength.