It follows from matrices of the form [[a, (-n)b], [b, a]] being closed under multiplication, and taking determinants. In more advanced language: For R a commut

It follows from matrices of the form [[a, (-n)b], [b, a]] being closed under multiplication, and taking determinants. In more advanced language: For R a commutative ring (like say, the integers) the following function f is a ring homomorphism f:R[√(-n)] -> M_2(R), f(a + b√(-n)) = [[a, (-n)b], [b, a]] Now take determinants.