Can a man say (As-Salaam Alaikum) when he enters the mosque?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

The correct act for the one who enters a mosque is to invoke blessings upon the Prophet Muhammad as narrated by Imam Abu Daawood who reported from Abu Humayd or Abu Usayd that the Prophet said: “Whoever enters a mosque should invoke blessings upon the Prophet and should say, O Allah! Open for me the doors of Your Mercy.”

Greeting by Salaam merely at the time of entering a mosque is not recommended except if there are people inside the mosque. If there are people, one may greet them for the Ahadeeth which teach Muslims to greet any gathering they join. But this greeting should be done only after performing the prayer of greeting the mosque.

Allah knows best.