Ruling on looking at and shaking hands with a father’s ex-wife after her divorce

The presenter: This is the last question in this message. Here is another one adjacent to this message. This was sent by the sender from Bahra, Abd al-Rahman Muhammad Hizam al-Shaybani. He says: Praise be to Allah, and may peace and blessings be upon the noblest of messengers.
As for what follows:
Please inform us, may Allah reward you, that my father married his cousin, his sister, and she remained in his care for five years without bearing any children, so he divorced her. After that, he married another wife, who is my mother. Is it permissible for me to greet her—meaning my father’s first wife—because she is my aunt, my father’s former wife? Is it permissible for me to greet her or not? Please inform us, may Allah reward you and prolong your lives?
Answer: Yes, your father’s wife is a mahram (a relative one may not marry) to you, whether she bore children or not. Your father’s wife, O questioner, is a mahram to you, whether she bore children from your father or not. Even if he only contracted a marriage with her without consummating it, she is still a mahram to you. This is because Allah said: [Surat al-Nisa: 22]. Therefore, the wives of fathers and grandfathers are mahrams merely by virtue of the marriage contract. If your grandfather or your father did not consummate the marriage, she is a mahram to you. And if he did consummate it and cohabit with her, she is a mahram to you all the more so, even if she did not bear children.
In summary: The wives of fathers and grandfathers are mahrams, whether they bore children from your fathers and grandfathers or not. And Allah (Exalted and Majestic is He) knows best. Yes.