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

theorem
  M2 is invertible & M1 is_similar_to M2 implies M1 is invertible
proof
  assume that
A1: M2 is invertible and
A2: M1 is_similar_to M2;
  consider M4 be Matrix of n,K such that
A3: M4 is invertible and
A4: M1=M4~*M2*M4 by A2;
  M4~ is invertible by A3;
  then M4~*M2 is invertible by A1,MATRIX_6:36;
  hence thesis by A3,A4,MATRIX_6:36;
end;
