Assignment:
Q1. a) Let R be a ring with 1 and let S=M2(R). If I is an field of S .show that there is an ideal J of R such that I consists of all 2X2 matrices over J.
b) Use the result of 1 a) to prove the following question. Let R be the ring of 2X2 matrices over reals; suppose that I is an ideal of R. Show that I =(0) or I=R.
Provide complete and step by step solution for the question and show calculations and use formulas.