I have a very simple two column list. Col-A is "Products" col-B is "Date
Purchase". Col-A is un-sorted and various products are repeated several
times. I want a lookup formula that would tell me the most recent date when a
particular product was purchased.

If col-A was sorted ascending, I could use
=LOOKUP(1E+100,INDEX(A2:B8,MATCH(A12,A2:A8,1),0)). Can someone please help.