True or false ?

  1. 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 ?
     
  2. jcsd
  3. Hi, Sam,
    if by matrix(a,b,a-b,a) you mean[tex]\left( \begin{array}{cc} a & b \\ a-b & 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 5-4 is not 4.
     
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