Why are those two lists not operating in the same way?

Question

I have created two lists in Python (lst_A and lst_B). I checked and those lists are equal. However, they act differently during value assignment, why is that? I would like to create a list as with procedure B but with 'behaviour' of list A.

lst_B = [[0]*2]*2
lst_A = [[0, 0], [0, 0]]
print(lst_A == lst_B)          # returns True

lst_B[0][0] = 1
print(lst_B)                   # returns [[1, 0], [1, 0]]

lst_A[0][0] = 1
print(lst_A)                   # returns [[1, 0], [0, 0]]