Python list of lists filled with duplicate rows after writing each entry

I am iterating over each entry of a list of lists and filling it with some unique number but the final list of lists contains identical rows. Here's a MWE:

x = [1,2,3,4]
y = [3,6,9,12]

Here I set up a list of lists filled with zeros.

m = [[0]*len(x)]*len(y)

And I print it to make sure it looks right.

[print(i) for i in m]

Now I iterate through each row and again through each item in the row and put the result of some calculation in each spot.

for i,ii in enumerate(y):
    for j,jj in enumerate(x):
        m[i][j] = ii*jj

But when I look at the final matrix it is just filled with repeated rows. Any help?

[print(i) for i in m]