stim (a) ca A(x) · A( y) = A( xy) o folosim pentru a dem:
asocia: A(x) ·[A(y) ·A(x) ] = [ A(x) ·A(y)] ·A(z)
A(x) · A(yz) = A(xy)·A(z)
A( xyz ) = A ( xyz)
elem neutru : matricea A( 1) = matricea unitate
A(x) ·A(e) = A(x)
A(xe) = A(x) daca xe = x , e=1
simetric : A(x) · A( x') = A( 1)
A( xx' ) = A( 1) ; xx' =1
x' =1 /x ; x∈ R*
matricea A ( 1 /x)
comut . A(x) ·A(y) = A(y)·A(x)
A( xy ) = A ( yx) ⇒ xy =yx , adevarat cu x, y ∈ R
