why can't I change only a single element in a nested list in Python [duplicate]

A strange behaviour indeed, but that's only because * operator makes shallow copies, in your case - shallow copies of [0, 0, 0] list. You can use the id() function to make sure that these internal lists are actually the same:

out=[[0]*3]*3
id(out[0])
>>> 140503648365240
id(out[1])
>>> 140503648365240
id(out[2])
>>> 140503648365240

Comprehensions can be used to create different lists as follows:

out = [ [0]*3 for _ in range(3) ]

Using * to duplicate elements in lists is a shallow copy operation, so you will end up with multiple references to the same mutable objects if you use this on a list that contains mutable objects.

Instead, use the following to initialize your nested list:

out = [[0]*3 for _ in range(3)]

You can see that with your method, each entry in out is actually a reference to the same list, which is why you see the behavior that you do:

>>> out = [[0]*3]*3
>>> out[0] is out[1] is out[2]
True