How to multiply combinations of two sets of pandas dataframe columns

I would like to multiply the combinations of two sets of columns

Let say there is a dataframe below:

import pandas as pd

df = {'A':[1,2,3], 'B':[4,5,6], 'C':[7,8,9], 'D':[0,1,2]}
df = pd.DataFrame(df)

Now, I want to multiply AC, AD, BC, BD
This is like multiplying the combination of [A,B] and [C,D]

I tried to use itertools but failed to figure it out.

So, the desired output will be like:

output = {'AC':[7,16,27], 'AD':[0,2,6], 'BC':[28,40,54], 'BD':[0,5,12]}
output = pd.DataFrame(output)

>Solution :

IIUC, you can try

import itertools

cols1 = ['A', 'B']
cols2 = ['C', 'D']

for col1, col2 in itertools.product(cols1, cols2):
    df[col1+col2] = df[col1] * df[col2]

print(df)

   A  B  C  D  AC  AD  BC  BD
0  1  4  7  0   7   0  28   0
1  2  5  8  1  16   2  40   5
2  3  6  9  2  27   6  54  12

Or with new create dataframe

out = pd.concat([df[col1].mul(df[col2]).to_frame(col1+col2)
                 for col1, col2 in itertools.product(cols1, cols2)], axis=1)

print(out)

   AC  AD  BC  BD
0   7   0  28   0
1  16   2  40   5
2  27   6  54  12