Multiple same values in Column A, need to find the greater date in column B

I'm stumped on a particular problem with some data that's imported to me. I have zero control over how the data is coming in. (Just to clarify that point).

I have two columns and 107,000 rows.

Column A has an ID#, Column B has the corresponding Date.

The issue I have is that Column A can have multiple identical values, and the corresponding date value in Column B has different or same dates.

I'm looking to add column C with a way to look up the cell in Column A, check it against the rest of column A, find any matches, and then return the Max/most recent date from column B for that ID#.