The proof of Lemma 1.5 contains a reference to the i j condition on the row

Question:

The proof of Lemma 1.5 contains a reference to the i ≠ j condition on the row combination operation.
(a) Write down a 2×2 matrix with nonzero entries, and show that the -1 ∙ p1 +p1 operation is not reversed by 1 ∙ p1 + p1.
(b) Expand the proof of that lemma to make explicit exactly where it uses the i ≠ j condition on combining.