Appending to 2D lists in Python

I've encountered what I think is a strange behavior in Python, and I'd like somebody to explain it if possible.

I've created an empty 2D list

listy = [[]]*3

print listy

[[], [], []]

The following works as I'd expect:

listy[1] = [1,2] yields [[], [1,2], []]

listy[1].append(3) yields [[], [1,2,3], []]

However, when I append to one of the empty lists, python appends to ALL of the sublists, as follows:

listy[2].append(1) yields [[1], [1,2,3], [1]].

Can anyone explain to me why this behavior occurs?