System under matrix addition (+) and matrix multiplication (.) is a field

Thread starter sam_0017
Start date Mar 27, 2012
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Addition Field Matrix Matrix multiplication Multiplication System

AI Thread Summary

The statement that the system {S,+,.} with S = { matrix (a,b,a-b,a)|a,b ∊ R} is not a field under matrix addition and multiplication is deemed false. The reasoning provided indicates that {S,+} forms an Abelian group, satisfying the necessary group properties. Additionally, {S,.} is also identified as an Abelian group. Therefore, the conclusion is that the system can indeed be considered a field based on these properties. Further discussion on this topic may be more appropriate in a dedicated math section.

Mar 27, 2012

sam_0017

Homework Statement

true or false ..
The system {S,+,.} with S = { matrix (a,b,a-b,a)|a,b ∊ R)
is not a field under matrix addition (+) and matrix multiplication (.)

i find that the statement is false .
since : 1. {S,+} is Abelian group.
2. {S,.} : is Abelian group.

is my finding is true ?

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Mar 28, 2012

physicsjock

i think you should post this in the math section

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