The solution looks like a bit of a hack, and it's problematic that it doesn't account for the scaling of the matrix. For example, it will return 0 if you input the identity matrix times 1e-30. It would be fine if you check any column for being exactly zero, but perhaps that isn't general enough.

Yes, you are right. Had a closer look and fixed it directly inside LU_comp where pivoting failed.
Added a LU_comp test, too. But, since I have no pytest experience on testing exceptions, this test looks more like a hack, too.

If you don't like the compact pytest.raises(Exception, function) notation, you can also use pytest.raises like this:

    with pytest.raises(MyException):
        do_something_wrong()

This checks that the expected exception is thrown somewhere within the "with"-block, and is actually the recommended notation in the pytest docs.

The updated fix looks good to me.