true or false ?by sam_0017 Tags: None 

#1
Mar2812, 01:08 AM

P: 24

true or false ..
The system {S,+,.} with S = { matrix (a,b,ab,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 ? 



#2
Mar2812, 07:39 AM

P: 688

Hi, Sam,
if by matrix(a,b,ab,a) you mean[tex]\left( \begin{array}{cc} a & b \\ ab & a \end{array} \right)[/tex]and multiplication is the usual matrix multiplication, then try to multiply two such matrices, to see that the result may not have the same form. For example,[tex]\left( \begin{array}{cc} 2 & 1 \\ 1 & 2 \end{array} \right)^2 = \left( \begin{array}{cc} 5 & 4 \\ 4 & 5 \end{array} \right)[/tex]but 54 is not 4. 


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