3 Define the set S of matrices by S = {A = (aij) € M₂ (R) : a11 = a22, a 12 = -a21}. It turns out that S is a ring, with the operations of matrix addition and multiplication. (a) Write down two examples of elements of S, and compute their sum and product. (b) Prove the additive and multiplicative closure laws for S. (c) Assume that M₂ (R) has already been proved to be a ring. If you wanted to prove that S was a ring, which axioms would follow immediately from the fact that M₂ (R) is a ring, and for which axioms would there be something else to check? [

3 Define the set S of matrices by S = {A = (aij) € M₂ (R) : a11 = a22, a 12 = -a21}. It turns out that S is a ring, with the operations of matrix addition and multiplication. (a) Write down two examples of elements of S, and compute their sum and product. (b) Prove the additive and multiplicative closure laws for S. (c) Assume that M₂ (R) has already been proved to be a ring. If you wanted to prove that S was a ring, which axioms would follow immediately from the fact that M₂ (R) is a ring, and for which axioms would there be something else to check? [

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.1: Operations With Matrices

Problem 77E

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