If you read the Bible, Luke: 20:26 it says: “while they were still talking about this, Jesus (A.S) himself stood among them and said to them, ‘PEACE BE WITH U’. and if you read it from Hebrew Bible it says, SHALOM ALAIKUM.
Luke 10:14 says: ‘ and into whatever house you shall enter, first say, ” PEACE BE TO THIS HOUSE.”
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And the Qur’an also says in Sura an-aam: 6:54, ‘ and when those who believe in our signs come to you (the believers in one and only God, Allah), say Salaam Alaikum (Peace be upon you.’
Also in John 20:26 says, ‘ after eight days again, his disciples were within, and Thomas with them. There came Jesus, the doors being shut, and stood in the midst and said, ‘PEACE BE UNTO YOU.’
It's really important for every Muslim to know. Nowadays even Muslims don't use this way of greeting…I remember when I'm at my home village, my family members are the only ones from where I hear the word "Assalam Alaikum" but when I leave for say 4 months, I wuill never be greeted or replied walaikum salaam…eh! what is going on Muslims??