Group duplicate column IDs in pandas dataframe

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Now there are a lot of similar questions but most of them answer how to delete the duplicate columns. However, I want to know how can I make a list of tuples where each tuple contains the column names of duplicate columns. I am assuming that each column has a unique name. Just to further illustrate my question:

df = pd.DataFrame({'A': [1, 2, 3, 4, 5],'B': [2, 4, 2, 1, 9],
                   'C': [1, 2, 3, 4, 5],'D': [2, 4, 2, 1, 9],
                   'E': [3, 4, 2, 1, 2],'F': [1, 1, 1, 1, 1]},
                   index = ['a1', 'a2', 'a3', 'a4', 'a5'])

then I want the output:

[('A', 'C'), ('B', 'D')]

And if you are feeling great today then also extend the same question to rows. How to get a list of tuples where each tuple contains duplicate rows.

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