Remove duplicates by columns A, keeping the row with the highest value in column B

I have a dataframe with repeat values in column A. I want to drop duplicates, keeping the row with the highest value in column B.

So this:

A B
1 10
1 20
2 30
2 40
3 10

Should turn into this:

A B
1 20
2 40
3 10

I’m guessing there’s probably an easy way to do this—maybe as easy as sorting the DataFrame before dropping duplicates—but I don’t know groupby’s internal logic well enough to figure it out. Any suggestions?