reserve i,n for Nat,
  K for Field,
  M1,M2,M3,M4 for Matrix of n,K;

theorem
  M1 is Self_Reversible implies M1 is Involutory
proof
  assume
A1: M1 is Self_Reversible;
  then M1 is invertible;
  then M1~ is_reverse_of M1 by MATRIX_6:def 4;
  then
A2: M1*M1~=1.(K,n) by MATRIX_6:def 2;
  M1*M1=M1*M1~ by A1;
  hence thesis by A2;
end;
