8. let salle &]: xy, 2 e R} a). Prove that (5, +,-) is a ring, where t’ and are the usual addition and multiplication of matrices. (You may assume standard properities of matrix Operations ) b). Let T be the set of matrices in 5 of the form { x so]. Prove that I is an ideal in the ring s. c). Let & be the function f: 5-71R, given by f[ 8 ] = 2 i prove that f is a ring homomorphism GIJ Explain why kerf = T, using the definition of kernel. d). Determine whether or not the quotient ring SIT is isomorphic to the ring R. Justify fully. your claim

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