a13. Show that the set of matrices of the formwhere a, b e R, is a fielda-under the operations of matrix addition and multiplication.

Answered: a Show that the set of matrices of the…

a Show that the set of matrices of the form where a, b e R, is a field -b a under the operations of matrix addition and multiplication.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.6: Matrices

Problem 23E: Prove that the set S={[abba]|a,b} is closed with respect to matrix addition and multiplication in...

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a
13. Show that the set of matrices of the form
where a, b e R, is a field
a
-
under the operations of matrix addition and multiplication.

Expert Solution

Step 1

Concept:

A field is a set with two operations called addition and multiplication (F, +, x), which satisfied following conditions:

Axioms of addition.
Axioms of multiplication.
Distributive properties.

Note:

Since square matrices always follows distributive law so we need to check first two properties.

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