How to add multiindex columns to existing df, preserving original index

I start with:

df
   0  1  2  3  4
0  5  0  0  2  6
1  9  6  5  8  6
2  8  9  4  2  1
3  2  5  8  9  6
4  8  8  8  0  8

and want to end up with:

df
         0  1  2  3  4
A  B  C
1  2  0  5  0  0  2  6
      1  9  6  5  8  6
      2  8  9  4  2  1
      3  2  5  8  9  6
      4  8  8  8  0  8

where A and B are known after df creation, and C is the original
index of the df.

MWE:

import pandas as pd
import numpy as np


df = pd.DataFrame(np.random.randint(10, size=(5, 5)))
df_a = 1
df_b = 2

breakpoint()

What I have in mind, but gives unhashable type error:

df.reindex([df_a, df_b, df.index])

>Solution :

Tru with pd.MultiIndex.from_product

df.index = pd.MultiIndex.from_product([[1],[2],df.index],names = ['A','B','C'])
df
Out[682]: 
       0  1  2  3  4
A B C               
1 2 0  7  0  1  9  9
    1  0  4  7  3  2
    2  7  2  0  0  4
    3  5  5  6  8  4
    4  1  4  9  8  1