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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