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

theorem Th10:
  for A being (Matrix of REAL), i,j being Nat st 
  [i,j] in Indices A holds (-A)*(i,j)=-(A*(i,j))
proof
  let A be (Matrix of REAL), i,j be Nat;
  assume
A1: [i,j] in Indices A;
  -A=(-1)*A by Th9;
  then (-A)*(i,j)= (-1)*(A*(i,j)) by A1,MATRIXR1:29;
  hence thesis;
end;
