Let R be a commutative ring with 1. Let M₂(R) be the 2 × 2 matrix ring over R and R[x] be the polyno- mial ring over R. Consider the subsets
s= a b | a,b€R and J = 0 b |a,b€R
0 a 0 0
of M₂ (R), and consider the function : R[x]- → M₂ (R) given for any polynomial p(x) = c0+c₁x+ ··· +cnx² € R[x]
∅(p(x))=c0 c1
0 c0
(1) Show that S is a commutative unital subring of M₂(R).