Greeting Salam to Non-Muslims: the Ignorant and the Non-Believers

The Quran describes Muslims as humble, wishing Salam to the Ignorant, and it commands that the Non-believer be wished Salam as well: 

Al-Quran 25:63 [Yusuf Ali] And the servants of (Allah) Most Gracious are those who walk on the earth in humility, and when the ignorant address them, they say, "Peace!";

Al-Quran 43:88-89 [Yusuf Ali] (Allah has knowledge) of the (Prophet's) cry, "O my Lord! Truly these are people who will not believe!" But turn away from them, and say "Peace!" But soon shall they know! 

May Allah guide us all to follow His commands, in letter and in spirit, and may Allah be well-pleased with us.