A real image is a set of points that act as another light source for the real object. It’s like a real replica of the object as far as the optics is concerned. So a real image is only formed when rays from different points on the object meet each other (converge).
Since rays are only converged by a concave mirror or a convex lens towards their center, rays can only meet below the X-axis if the object is above the X-axis, hence the real image is formed inverted in all planes with respect to the object.
So the real image is always inverted.