reserve i,j,n for Nat,
  K for Field,
  a for Element of K,
  M,M1,M2,M3,M4 for Matrix of n,K;
reserve A for Matrix of K;

theorem
  for K being Ring
  for M1 being Matrix of n,K
  holds M1 is Orthogonal implies (M1@)*M1=M1*(M1@)
proof
  let K be Ring;
  let M1 be Matrix of n,K;
  assume
A1: M1 is Orthogonal;
  then (M1@)*M1=1.(K,n) by Th43;
  hence thesis by A1,Th42;
end;
