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 Th3:
  for K being Ring, M1 being Matrix of n,K
  holds M1 commutes_with 0.(K,n,n)
proof
  let K be Ring;
  let M1 be Matrix of n,K;
A2: len M1 = n & width M1=n by MATRIX_0:24;
    then (0.(K,n,n))*M1=0.(K,n,n) by Th1;
    hence thesis by A2,Th2;
end;
