Eine Art Kommutativgesetz für Matrizen

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Beispiel:

http://maxima-online.org/?inc=r-1357806164

(%i1) A:matrix([2,-3,-5],[-1,4,5],[1,-3,-4]);
[ 2 - 3 - 5 ]
[ ]
(%o1) [ - 1 4 5 ]
[ ]
[ 1 - 3 - 4 ]
(%i2) B:matrix([-2,3,5],[1,-3,-8],[-1,7,5]);
[ - 2 3 5 ]
[ ]
(%o2) [ 1 - 3 - 8 ]
[ ]
[ - 1 7 5 ]
(%i3) is(transpose(A.B)=transpose(B).transpose(A));
(%o3) true
(%i4) AB:A.B;
[ - 2 - 20 9 ]
[ ]
(%o4) [ 1 20 - 12 ]
[ ]
[ - 1 - 16 9 ]
(%i5) LI:transpose(AB);
[ - 2 1 - 1 ]
[ ]
(%o5) [ - 20 20 - 16 ]
[ ]
[ 9 - 12 9 ]
(%i6) TA:transpose(A);
[ 2 - 1 1 ]
[ ]
(%o6) [ - 3 4 - 3 ]
[ ]
[ - 5 5 - 4 ]
(%i7) TB:transpose(B);
[ - 2 1 - 1 ]
[ ]
(%o7) [ 3 - 3 7 ]
[ ]
[ 5 - 8 5 ]
(%i8) RE:TB.TA;
[ - 2 1 - 1 ]
[ ]
(%o8) [ - 20 20 - 16 ]
[ ]
[ 9 - 12 9 ]
(%i9) is(LI=RE);
(%o9) true
(%i10)