Iterating over empty 2d vs non-empty python

I want to iterate over a 2d python list. However, I have noticed a difference when it iterates over an empty 2d array vs a nonempty 2d array. For example

    mat = [[]] * n
    print("initial", mat)
    
    count = 0
    for row in mat:
        print("row:", row)
        for _ in range(2):
            print(_)
            row.append(count)
            count += 1
            print(mat)
        print("\n")
    return mat
mat = empty(2)

This is what it prints. It is appending the count to both the sub-arrays instead of just one

initial [[], []]
row: []
0
[[0], [0]]
1
[[0, 1], [0, 1]]


row: [0, 1]
0
[[0, 1, 2], [0, 1, 2]]
1
[[0, 1, 2, 3], [0, 1, 2, 3]]

However when I change the code to this

def nonempty(n):
    mat = [['a'],['b']]
    print("initial", mat)
    
    count = 0
    for row in mat:
        print("row:", row)
        for _ in range(2):
            print(_)
            row.append(count)
            count += 1
            print(mat)
        print("\n")
    return mat
mat = empty(2)

This is what it prints

initial [['a'], ['b']]
row: ['a']
0
[['a', 0], ['b']]
1
[['a', 0, 1], ['b']]


row: ['b']
0
[['a', 0, 1], ['b', 2]]
1
[['a', 0, 1], ['b', 2, 3]]

In this case, it only changes one sub array at a time instead of two. Can anyone tell me why this is happening. Is it because of how python lists work?