2-1.mws

2-1 Show that trace of AB = trace of BA

> restart;

> A:=Matrix([[a,b],[c,d]]);

A := _rtable[11743124]

> B:=Matrix([[p,q],[r,s]]);

B := _rtable[11956012]

> A.B;

_rtable[7514356]

> B.A;

_rtable[7663532]

> trace(A.B);

> ?trace

> ?Trace;

> with(linalg);

Warning, the protected names norm and trace have been redefined and unprotected

[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp,...
[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp,...
[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp,...
[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp,...
[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp,...
[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp,...
[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp,...
[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp,...
[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp,...
[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp,...

> trace(A.B);

a*p+b*r+c*q+d*s

> trace(B.A);

a*p+b*r+c*q+d*s

> trace(A.B-B.A);

0