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

theorem
  M1 is Idempotent Orthogonal implies M1 is symmetric
proof
  assume
A1: M1 is Idempotent Orthogonal;
  then M1 is invertible by MATRIX_6:def 7;
  then M1=1.(K,n) by A1,Th10;
  hence thesis;
end;
