No, you still have to try to shuffle to get a non-zero pivot element. Only if you cannot get a non-zero pivot element (because there only remain zeros in the column position), you are allowed to abort (then there exist multiple solutions).
No, you still have to try to shuffle to get a non-zero pivot element. Only if you cannot get a non-zero pivot element (because there only remain zeros in the column position), you are allowed to abort (then there exist multiple solutions).