You can merge two dataframes based on columns df1['A'] and df2['B'] using the pandas merge() function as follows:
```arduino
merged_df = pd.merge(df1, df2, left_on='A', right_on='B')
```

This will merge the two dataframes df1 and df2 based on the columns 'A' in df1 and 'B' in df2, creating a new dataframe merged_df. By default, the merge function performs an inner join, which means only the rows that have matching values in both dataframes will be included in the merged dataframe. You can also specify the type of join (inner, left, right or outer) using the how parameter.

If you want to merge on multiple columns, you can pass a list of column names to the left_on and right_on parameters:
```css
merged_df = pd.merge(df1, df2, left_on=['A', 'C'], right_on=['B', 'D'])
```

This will merge the two dataframes based on the columns 'A' and 'C' in df1 and 'B' and 'D' in df2.
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