A=(({{-9.9999, -10}, {10, 10.0001}}));
iA = 
        Inverse[A];
Print["A = ", 
        MatrixForm[
          A]];
\(Print[\*""(A^(-2)) (A^2) = "", MatrixForm[iA . iA . A . A]];\)

Asym = Rationalize[A];
Print["A = ", MatrixForm[Asym]];
iAsym = Inverse[Asym];
\(Print[\*""\!\(A\^\(-2\)\) \!\(A\^2\) = "", 
      MatrixForm[iAsym . iAsym . Asym . Asym]]\)