8. Let S be the set of all 2 x 2 matrices of the form where x is an integer. Assume that S is a ring with respect to matrix addition and multiplication. (a) Is S a commutative ring? (b) Does S have a unity? (c) Does S have zero divisors?

8. Let S be the set of all 2 x 2 matrices of the form where x is an integer. Assume that S is a ring with respect to matrix addition and multiplication. (a) Is S a commutative ring? (b) Does S have a unity? (c) Does S have zero divisors?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.1: Ideals And Quotient Rings

Problem 28E: 28. a. Show that the set is a ring with respect to matrix addition and multiplication. b. Is...

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Question

8. Let S be the set of all 2 x 2 matrices of the form
where x is an integer. Assume that S is a
ring with respect to matrix addition and multiplication.
(a) Is S a commutative ring?
(b) Does S have a unity?
(c) Does S have zero divisors?

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