How to check if Up button enabled?

Some where in code I add

ActionBar ab = ((AuthActivity) getActivity()).getSupportActionBar();
    if (ab != null) {
      ab.hide();
      ab.show();
      ab.setTitle(R.string.auth_tt_title);
      ab.setDisplayHomeAsUpEnabled(true);
    }

Later, I add fiew fragments one of which may change title and display home button.Thus, I wat to save state for ActionBar before I made changes, to be able to restore it asfter fragment will be gone. I can get title as

private String getAbStatus(AppCompatActivity activity) {
    String title="";
    boolean visible;
    ActionBar ab = activity.getSupportActionBar();
    if (ab != null) {
      if (ab.getTitle() != null) title = ab.getTitle().toString();
    }
    return title;
  }

But how can I get state of HomeAsUp?