Can you shake hands with an old woman?

The majority of Jurists hold the correct opinion that a man is not to touch any part of the body of a woman who is alive and a stranger whether she is young or old.

The Hanafis incorrectly say that it is permissible to shake hands with an old woman and touch her hand because there is no fear of fitnah in doing so.

The majority have based their correct opinion on the following hadith

'Aishah (may Allaah be pleased with her) said that the Messenger of Allaah never touched the hand of a woman...

[Sahih al-Bukhaari]

Additionally, touching the hand of a woman is much worse than looking at her when it comes to desire.

Reference(s):

Kuwaiti Encyclopedia of Fiqh
Volume 37 Page 286