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

theorem
  M1 is Idempotent & M2 is Idempotent & M1 is invertible implies M1*M2
  is Idempotent
proof
  assume that
A1: M1 is Idempotent and
A2: M2 is Idempotent and
A3: M1 is invertible;
  M1=1.(K,n) by A1,A3,Th10;
  hence thesis by A2,MATRIX_3:18;
end;
