answer no.5 Let M₂ (R) be the set of 2 x 2 matrices with real number entries, i.e.,M₂(R) = {[a b]a,b,c,d ER}.Define matrix addition and matrix multiplication in M₂(R) as followsa1b₁az b₂a₁ + a₂ b₁ + b₂=[C1d₁0₂ d₂;] + [][b₁ az b₂d₂=a₁a₂+ b₁c₂ a₁b₂ + b1d₂c₁a₂+d₂c₂ c₁b₂+did₂d₁ C₂01C1]. 4. Is M₂ (R) a field? Justify.I Y5. Show that T =- {[ 8 ] |z, y, z € R} is a subring of M2 (R).2

Answered: 4. Is M₂ (R) a field? Justify. I 5.…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 22E: Prove that if R and S are fields, then the direct sum RS is not a field. [Type here][Type here]

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4. Is M₂ (R) a field? Justify. I 5. Show that T = = { [ ² ] 12,9₁² € R} i 2 is a subring of M₂ (R).