Difference between assignment and compound operators in Python

Please look into the code below

def double(arg):
    print("Before: ", arg)
    arg = arg * 2
    print("After: ", arg)

I was studying Head first Python, and I came to this section where they were discussing about pass by value and pass by reference. If we invoke above function with a list as argument such as:

num = [1,2,3]
double(num)
print(num)

The output is :-

Before:  [1, 2, 3]
After:  [1, 2, 3, 1, 2, 3]
[1, 2, 3]

Which seems fine, considering the fact that arg in function double is a new object reference. So the value of num did not change.

But if I use compound operators instead of assignment operators, things work differently as shown:

def double(arg):
    print("Before: ", arg)
    arg *= 2
    print("After: ", arg)

num = [1,2,3]
double(num)
print(num)

The output that I get for this is:

Before:  [1, 2, 3]
After:  [1, 2, 3, 1, 2, 3]
[1, 2, 3, 1, 2, 3]

Why does this happen? I used to think a*=2 and a = a*2 are same. But what's going on in here?

Thanks