Update particular grid cell in Python 3

Question

I have very simple example in Python:

class Solution(object):

    def grid(self, m, n):
        grid = [[0] * n] * m
        grid[0][0] = 1
        print(grid)


Solution().grid(5, 3)

When I run this code, it prints [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 0, 0]]

I'd expect it'd print [[1, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]

I'm running Python 3.8.5

What am I missing here?