Is this an actual physics question, or a zen koan? There really is such a thing as anti-matter, predicted by Dirac in 1928 & discovered in 1932. Antiparticles relate to electric charge: Each kind of particle has a corresponding anti-particle of opposite charge. Oppositely-charged quarks and anti-quarks may combine as well, which is why neutrons & anti-neutrons both have zero charge but are not identical particles.
An electron has -1 charge so an anti-electron (aka positron) has a +1 charge, but is otherwise identical in mass and spin. Similarly antiprotons are negatively charged versions of the normally positively charged proton. Positrons and antiprotons may combine to form antihydrogen. Because of charge symmetry the laws of physics & chemistry are pretty much the same for antimatter as matter, with all the usual elements and molecules, so there could be entire antimatter galaxies with antimatter planets harboring antimatter people.
A physicist (Feynman?) suggested that if you greet an alien & he extends his left arm instead of right, don’t shake his hand! Parity reversal implies that he’s made of antimatter – touch and you’ll both be annihilated in a huge burst of gamma ray energy. This is the basis for sci-fi spaceship propulsion using matter-antimatter annihilation as an energy supply (the trick being to contain and control the flow of antimatter using equipment made of ordinary matter).
A persistent cosmological enigma is why matter seems to greatly predominate over antimatter in the observable universe? – some kind of broken symmetry.
Dark matter (needed to explain the gravitational behavior of galaxies) and dark energy (needed to explain the accelerating expansion of the cosmos) are still huge mysteries as well, but whatever they are they can’t simply be antimatter, which is known to be luminous by interacting with photons just as ordinary matter does. Antimatter is not “dark.”
The idea that the existence of an object always leaves behind a negative “hole” from whence it came has actual physical underpinnings in the form of so-called negative energy or vacuum energy, which I first read about in The Elegant Universe by Brian Greene, 2000.
So far as I know, there is no “anti-dark-matter” or “anti-dark-energy”, i.e., I don’t think those terms have meaning to a physicist.
As it happens I’m presently partway through A Universe from Nothing: Why There Is Something Rather than Nothing by theoretical physicist Lawrence Krauss, 2011. Unfortunately I haven’t yet gotten to the part about dark energy or – the ultimate mystery – the origin of the big bang.