Random Shuffling A matrix

import random

matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]] # Assume a list is given

for row in range(len(matrix)):
    for column in range(len(matrix[row])):
        i = random.randint(0, len(matrix) - 1)
        j = random.randint(0, len(matrix[row]) - 1)

        # Swap matrix[row][column] with matrix [i][j]
        matrix[row][column], matrix[i][j] = matrix[i][j], matrix[row][column]


for row in range(len(matrix)):
    for column in range(len(matrix[row])):
        print(matrix[row][column], end=" ")

    print()