Excel: Does it return the last date for each value in another column?

In an Excel spreadsheet, I have a customer ID (column A) and several purchase dates (column B) for each customer. Does it look like this:

CustomerID   Purchase Date
1               1/1/20
1               1/6/20
1               1/18/20
2               1/15/20
2               1/26/20
3               1/14/20
3               1/7/20
3               1/28/20
4               2/5/20
5               1/16/20
5               1/9/20
...

What I would like to do: find a formula to put in column C that will tell me if the purchase date is the largest / most recent for each customer ID. I'm looking to create something that looks like this:

CustomerID   Purchase Date    FORMULA
1               1/1/20           NO
1               1/6/20           NO
1               1/18/20          YES
2               1/15/20          NO
2               1/26/20          YES
3               1/14/20          NO
3               1/7/20           NO
3               1/28/20          YES
4               2/5/20           YES
5               1/16/20          YES
5               1/9/20           NO
...

The ultimate goal is to keep only the most recent records for each customer (you could simply delete all rows with & # 39; NO & # 39;). Any ideas?