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 Th9:
  for R being Ring
  holds (1.(R,n))~ = 1.(R,n) & 1.(R,n) is invertible
proof
  let R be Ring;
  (1.(R,n))*(1.(R,n))=1.(R,n) by MATRIX_3:18;
  then 1.(R,n) is_reverse_of 1.(R,n);
  hence thesis by Def4;
end;
