reserve i,j for Nat;

theorem Th53:
  for x being FinSequence of REAL,A being Matrix of REAL st len A>
  0 & width A>0 & (width A=len x or len (A@)=len x) holds A*x = x*(A@)
proof
  let x be FinSequence of REAL,A be Matrix of REAL;
  assume that
A1: len A>0 and
A2: width A>0 and
A3: width A=len x or len (A@)=len x;
  len (A@) = width A & width (A@)=len A by A2,MATRIX_0:54;
  then ((A@)@)*x=x*(A@) by A1,A2,A3,Th52;
  hence thesis by A1,A2,MATRIX_0:57;
end;
