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

by

This takes the last. Not the maximum though:

In [10]: df.drop_duplicates(subset="A", keep="last")
Out[10]: 
   A   B
1  1  20
3  2  40
4  3  10

You can do also something like:

In [12]: df.groupby('A', group_keys=False).apply(lambda x: x.loc[x.B.idxmax()])
Out[12]: 
   A   B
A       
1  1  20
2  2  40
3  3  10

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