The Ruling on Shaking Hands with a Disbeliever

What is the ruling on shaking hands with a disbeliever if he is the one who initiates the handshake?
If a disbeliever extends his hand for a handshake, shake hands with him; for the Prophet (peace and blessings be upon him) only forbade initiating with them, meaning that we should not be the ones to start by greeting them. However, if they initiate with us or shake our hands, we must shake hands with them. But we do not extend our hands to them for a handshake ourselves. If a disbeliever greets you, return his greeting. If he shakes your hand, extend your hand to him. If he does not greet you, do not greet him. If he does not shake your hand, do not shake his hand.To you is this noble verse, may Allah bless you: [Surat al-Nisa: 86] It did not say: "When some of you greet one another" (if you are greeted) So any person who greets us, even if he is the most disbelieving of Allah's servants, we return to him like his greeting or more. But the better course with non-Muslims is not to return a better greeting; return to him like his greeting; for if you return a better greeting to him, you increase his good and he rejoices in it.