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

[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 ?

 

[physicsjock]

i think you should post this in the math section