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2 let m2z denote the ring of 2x2 matrices with...

Question: 2 let m2z denote the ring of 2x2 matrices with...

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2. Let M2(Z) denote the ring of 2x2 matrices with integer entries. (You do not have to prove that M2(Z) is a ring.) Now let U be the set of upper triangular 2x2 matrices with entries in Z. That is, U is comprised of all matrices of the form a. for a, b, c e2z (a) Prove that U is a unital subring of M2(Z). (b) Find all of the idempotents of U (c) Prove that U is not commutative.

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