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
  for K being Ring
  for M1,M2 being Matrix of n,K
  holds M1 is Orthogonal & M1 commutes_with M2 implies M1@ commutes_with M2
by Th41;
