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 Th7:
  for R being Ring
  for M1 being Matrix of n,R
  holds M1 commutes_with 1.(R,n)
proof
  let R be Ring;
  let M1 be Matrix of n,R;
  M1 = M1 * (1.(R,n)) & M1 = 1.(R,n) * M1 by MATRIX_3:18,19;
  hence thesis;
end;
