BUG: .mul on multi index columns doesnt work.

[Andre-Medina]

Pandas version checks

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

import pandas as pd
data = pd.DataFrame(
    {
        "state": (["vic", "nsw", "tas"] * 3 + ['vic'])*2,
        "colour": ['red'] * 10 + ['blue'] * 10,
        "month": ['mar', 'sep'] * 10,
        "year": [2020, 2020, 2020, 2021, 2021, 2021, 2022, 2022, 2022, 2023] * 2,
        "value": range(20),
    }
).set_index(['state','colour','year', 'month']).unstack(['state','year','month'])['value']
data.pipe(print)
"""
state    vic  nsw  tas  vic  nsw  tas  vic  nsw  tas  vic
year    2020 2020 2020 2021 2021 2021 2022 2022 2022 2023
month    mar  sep  mar  sep  mar  sep  mar  sep  mar  sep
colour                                                   
blue      10   11   12   13   14   15   16   17   18   19
red        0    1    2    3    4    5    6    7    8    9
"""

scaler = pd.DataFrame(
    [
        {"year": 2020, "month": "mar", "scale": 0.5},
        {"year": 2020, "month": "sep", "scale": 0.5},
        {"year": 2021, "month": "mar", "scale": 0.5},
        {"year": 2021, "month": "sep", "scale": 0.5},
        {"year": 2022, "month": "mar", "scale": 0.5},
        {"year": 2022, "month": "sep", "scale": 0.5},
        {"year": 2023, "month": "mar", "scale": 0.5},
        {"year": 2023, "month": "sep", "scale": 0.5},
    ]
).set_index(['year','month'])['scale']
scaler.pipe(print)
"""
year  month
2020  mar      0.5
      sep      0.5
2021  mar      0.5
      sep      0.5
2022  mar      0.5
      sep      0.5
2023  mar      0.5
      sep      0.5
Name: scale, dtype: float64
"""

mul_on_cols = data.mul(scaler, axis = 1)
mul_on_cols.pipe(print)
"""
state   vic  tas  nsw       vic  tas  vic  tas  nsw  NaN  vic
year   2020 2020 2020 2021 2021 2021 2022 2022 2022 2023 2023
month   mar  mar  sep  mar  sep  sep  mar  mar  sep  mar  sep
colour                                                       
blue    NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN
red     NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN
"""

mul_on_index = data.T.mul(scaler, axis = 0).T
mul_on_index.pipe(print)
"""
state   vic  tas  nsw       vic  tas  vic  tas  nsw  NaN  vic
year   2020 2020 2020 2021 2021 2021 2022 2022 2022 2023 2023
month   mar  mar  sep  mar  sep  sep  mar  mar  sep  mar  sep
colour                                                       
blue    5.0  6.0  5.5  7.0  6.5  7.5  8.0  9.0  8.5  NaN  9.5
red     0.0  1.0  0.5  2.0  1.5  2.5  3.0  4.0  3.5  NaN  4.5
"""

Issue Description

using .mul on multi index columns fails, but on multi index rows, works as expected. View screenshots and code example.

Expected Behavior

Refer to screenshots and example

Installed Versions

INSTALLED VERSIONS

commit : 0691c5c
python : 3.10.16
python-bits : 64
OS : Linux
OS-release : 5.15.167.4-microsoft-standard-WSL2
Version : #1 SMP Tue Nov 5 00:21:55 UTC 2024
machine : x86_64
processor :
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.2.3
numpy : 1.26.0
pytz : 2024.1
dateutil : 2.9.0.post0
pip : 25.0.1
Cython : None
sphinx : None
IPython : 8.17.2
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : 4.13.3
blosc : None
bottleneck : None
dataframe-api-compat : None
fastparquet : None
fsspec : 2025.2.0
html5lib : None
hypothesis : None
gcsfs : 2025.2.0
jinja2 : 3.1.5
lxml.etree : 5.3.0
matplotlib : 3.10.0
numba : 0.61.0
numexpr : None
odfpy : None
openpyxl : 3.1.5
pandas_gbq : None
psycopg2 : 2.9.9
pymysql : None
pyarrow : 17.0.0
pyreadstat : None
pytest : 8.3.4
python-calamine : None
pyxlsb : 1.0.10
s3fs : None
scipy : 1.15.2
sqlalchemy : 2.0.38
tables : None
tabulate : 0.9.0
xarray : 2025.1.2
xlrd : 2.0.1
xlsxwriter : 3.2.2
zstandard : 0.23.0
tzdata : 2025.1
qtpy : None
pyqt5 : None