DS-1000 / 52 / Sample dataframe:

prompt

Problem:
Sample dataframe:
df = pd.DataFrame({"A": [1, 2, 3], "B": [4, 5, 0]})

I'd like to add inverses of each existing column to the dataframe and name them based on existing column names with a prefix, e.g. inv_A is an inverse of column A and so on.
Notice that 0 has no inverse and please keep it in inv_A
The resulting dataframe should look like so:
result = pd.DataFrame({"A": [1, 2, 3], "B": [4, 5, 0], "inv_A": [1/1, 1/2, 1/3], "inv_B": [1/4, 1/5, 0]})

Obviously there are redundant methods like doing this in a loop, but there should exist much more pythonic ways of doing it and after searching for some time I didn't find anything. I understand that this is most probably a duplicate; if so, please point me to an existing answer.

A:
<code>
import pandas as pd


df = pd.DataFrame({"A": [1, 0, 3], "B": [4, 5, 6]})
</code>
result = ... # put solution in this variable
BEGIN SOLUTION
<code>