The hadith is authentic. The sunnah is to shake hands with Muslims you often see as a form of greeting.

Anas ibn Maalik (may Allaah be pleased with him) said: A man said:??O Messenger of Allaah, when one of us meets his brother or his friend, should he bow to him???He said:??No.??He said:??Should he embrace him and kiss him???He said:??No.??He said:??Should he take his hand and shake hands with him???He said:??Yes.?? [This hadeeth was classed as hasan by al-Albaani in Saheeh Sunan al-Tirmidhi] Please explain.

Commentary on Hadeeth | October 21, 2015 8:16 pm
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Ya Shaykh , Is the following hadith authentic?: Abdullah Ibn-Umar related that once, HE SAW THE PROPHET SHOWING `IRAQ WITH HIS HAND, AND SAYING: “THE FITNA IS HERE, THE FITNA IS HERE, THE FITNA IS HERE, THREE TIMES, IT IS FROM HERE THAT WILL APPEAR THE DEVIL’S HORNS,” (sahih) (Reference:-Musnad-e-Ahmad Vol.10 Page.391 Hadith.6302 or 6129, Isnad considered Sahih by the Muhaddith Ahmad Shakir al-Masry)
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Sheikh, I apologize for being questioning the same issue regarding hair dye. Sheikh I don’t understand one thing, why it was mentioned in hadith of father of Abu Bakar (RA) “Complete Hair” was white when Prophet (PBUH) told him to dye. Does it mean that reward of dying hair will be accountable when once complete hair is white?