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 holds 1.(K,n) is Orthogonal
proof
  let K be Ring;
A1: (1.(K,n))@=1.(K,n) by Th11;
  (1.(K,n))~=1.(K,n) & 1.(K,n) is invertible by Th9;
  hence thesis by A1;
end;
