When you have 2D array, shuffle functionality in python numpy does the trick only for rows, the following gist is how to randomly shuffle rows and columns

shuffle_by_rows_columns.py

import numpy as np

# Lets suppose you have a 2D array 
c = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])

# Suffle it for rows and columns 
np.random.permutation(np.random.permutation(c.transpose()).transpose())