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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem
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Prove that the set S = { [ a b b a ] | a , b } is closed with respect to matrix addition and multiplication in M 2 ( ) .

To determine

To prove: The set S={[abba]|a,b} is closed with respect to matrix addition and multiplication in M2().

Explanation

Given information:

The set S={[abba]|a,b}.

Formula used:

(1) Addition in Mm×n() is defined by

[aij]m×n+[bij]m×n=[cij]m×n, where cij=aij+bij.

(2) Definition: Matrix multiplication

The product of m×n matrix A over and n×p matrix B over is m×p matrix C=AB, where the element cij in row i and column j of AB is found by using the elements in row i of A, and the elements in column j of B in the following manner:

columnjofBcolumnjofCrowiofA[ai1ai2ai3ain][b1jb2jb3jbnj]=[cij]rowiofC

Where cij=ai1b1j+ai2b2j++ainbnj

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