Theorema aureum — 2

In the first part of this article, we had introduced the notion of quadratic reciprocity and dwelt briefly on its history, which goes back all the way to the work of Fermat. Then we discussed the Law of Quadratic Reciprocity (‘QRL’), which Gauss named Theorema Aureum . Following this, we gave a not too well known proof of the QRL, due to G Rousseau. Now we give two more proofs of the QRL, drawing respectively from ideas in linear algebra and field extensions ; they too are not very well known.