# true or false ?

by sam_0017
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 P: 24 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 ?
 P: 688 Hi, Sam, if by matrix(a,b,a-b,a) you mean$$\left( \begin{array}{cc} a & b \\ a-b & a \end{array} \right)$$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,$$\left( \begin{array}{cc} 2 & 1 \\ 1 & 2 \end{array} \right)^2 = \left( \begin{array}{cc} 5 & 4 \\ 4 & 5 \end{array} \right)$$but 5-4 is not 4.

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