Can space exist without matter or energy? Is it possible for the space to exist without matter or energy?
 A: The link is a generic education site for NASA for a gravitational probe. It is true that there is no observational evidence that space, gravity and spacetime, or time exists without all of them existing. How could there be, we live in the whole universe which has it all. That is a very simplistic notion, but clearly, in that context, true. 
But it leaves a lot to be explained and if you will, caveated.
It is also true, though not stated, that gravity and matter and spacetime are related by Einsteins Field Equations (EFE), in simplified units and ignoring the dark energy, 
$G\mu\nu$ = 8$\pi T\mu\nu$
See the whole treatment in Wikipedia at https://en.m.wikipedia.org/wiki/Einstein_field_equations
where G is the Einstein tensor that is constructed from spacetime metric elements and up to second space and time derivatives, and T is the matter-energy stress energy tensor that incorporates all matter. So, if one is nonzero the other also is nonzero. But existence is a different concept: tthe stress energy tensor can be zero in some region of spacetime, and so G will also be zero. But spacetime can then be simply Minkowski spacetime, i.e., no curvature. That means it exists, it is simply not curved. Big difference from not existing. 
Scientifically that's a fact, and we observe it all the time in regions where there is no matter-energy, and where any such matter energy is very far from what we are looking at. In many lab experiments we can assume spacetime is Minkowski, no curvature, and no gravity. It's a good enough approximation. 
In fact, the EFE allows solution with the right boundary conditions where there is no matter-density, but there is gravity in the form of gravitational waves, and spacetime has curvature. Not a problem. On the other hand it is also true that, ignoring dark energy, the universe with no matter-energy anywhere is flat Minkowski, no gravity, no curvature. Even worse, with the dark energy which seems to be energy from the spacetime vacuum, with no matter or other energy around, it turns out the universe would also be curved, with the solution being a deSitter universe, a spacetime with curvature. Trillions of years from now most energy and matter will have been diluted out, and that's what the universe would look like
Well, even worse, at very very high energies or small size scales, the so called Planck scale, we don't know what spacetime looks like, nor matter, and it's all a current research topic in quantum gravity. So, not exists is really not a scientific fact, but what is it in super-extreme cases is a good question. See, for Quantum Gravity, https://en.m.wikipedia.org/wiki/Quantum_gravity
So it's a statement that one has to be careful with. If a scientific statement it's got all kinds of caveats. If a philosophical statement it does NOT belong in a scientific site.
A: 
Is it possible for the space to exist without matter or energy?

As a possible mathematical model of nature,  yes.
Proof: Newtonian gravity , a classical very successful model, i.e. predictive and not only descriptive. General Relativity which posits that matter and energy form space time , reduces to Newtonian gravity at the interface, where GR effects are below the accuracy of measurements.
The model of General Relativity cannot exist without matter or energy, they have to exist , otherwise  all space time would be uniformly 0 for all values of space and time.
Is the GR model an ultimate model for space time? No, because  quantization of gravity changes it. If the encompassing theory is a string theory, again particles are necessary and particles are matter and have energy. 
From there on, one would have to wait for new observations and experiments, but at present it seems that matter and energy are tied up with space and time, starting from the frameworks where special relativity has to be used.
