Alhamdulilahi wa salaatu wa salaamu àlaa Rasuulullah.
According to a hadith narrated by Muslim, the our noble Prophet Mohammed( peace and blessings be upon Him) Said as Muslims we should not INITIATE the greetings of salaam to Jews or Christians.
However if they initiate by saying As-saam alaykum meaning death be upon you or the salaam is not clear, we should respond by saying Wa alaykum( and upon you).
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In conclusion by view of majority of scholars when a non Muslim initiate salaam and is very clear a Muslim can also respond correctly( wa alaikum salaam) but when the salaam is not clear the response should be wa alaykum or alayk.
Allah knows best. Assa laamu alaikum
–GIBRILL ABDUL HAMID