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 Th8:
  for R being Ring
  for M1,M2,M3 being Matrix of n,R
  holds M2 is_reverse_of M3 & M1 is_reverse_of M3 implies M1=M2
proof
  let R be Ring;
  let M1,M2,M3 be Matrix of n,R;
A1: width M1=n & width M3=n by MATRIX_0:24;
A2: len M2=n & len M3=n by MATRIX_0:24;
  assume that
A3: M2 is_reverse_of M3 and
A4: M1 is_reverse_of M3;
  M1=M1*(1.(R,n)) by MATRIX_3:19
    .=M1*(M3*M2) by A3
    .=(M1*M3)*M2 by A1,A2,MATRIX_3:33
    .=(1.(R,n))*M2 by A4
    .=M2 by MATRIX_3:18;
  hence thesis;
end;
