### Commutative Rings, Ideals, Kernels, Matrices and Injective and Surjective Ring Homomorphisms

If n Є R and R is a commutative ring we indicate by Mn(R) the ring of allnxn entries wrt the usual operations on matrices. If n>1 this ring is commutative even if R is. Let S={(aij)ЄMn(R)|i≠j=>aij=0} Let k be an integer 1≤k≤n. Show that a) S is a commutative subring of Mn(R) b) The function f: S