reserve x for set,
  D for non empty set,
  k,n,m,i,j,l for Nat,
  K for Field;

theorem Th71:
  for A be Matrix of n,REAL holds A*(1_Rmatrix(n))=A
proof
  let A be Matrix of n,REAL;
A1: n=len A by MATRIX_0:def 2;
  now
    per cases;
    case
      n<>0;
      hence n=width A by A1,MATRIX_0:20;
    end;
    case
      n=0;
      hence n=width A by A1,MATRIX_0:def 3;
    end;
  end;
  hence thesis by Th67;
end;
