Little is known of the being known as the Anti-Matter Man. It is known he came from an anti-matter universe- presumably Qward, but not specified- as an explorer, and regarded the opposition he came under from the Justice League and the Justice Society as typical trials of space travel. This is only discerned through mind reading, however, as he never speaks in his appearance.
One of Ray Palmer's students, Enrichetta Negreni, invented a device to shrink space so space travel would be easier. Instead, it somehow began affecting the universes of Earths-1 and 2, so people and objects began switching places, including Blockbuster and Solomon Grundy, as well as placing the two Earths in the same universe.
During this incursion, the Anti-Matter Man was also drawn into the positive matter universe. The Spectre began desperately attempting to prevent him from making contact on one of the Earths, which would result in the annihilation of said Earth. The Anti-Matter Man began effecting him in bizarre, slapstick ways, such as enlarging the Spectre's head. Eventually, the Spectre is reduced to physically holding the two Earths apart while the Anti-Matter Man creeps closer.
After dealing with the two bruisers, Dr. Fate magically discerns the threat and, using his magic, allows the JLA and JSA to deal with the Anti-Matter Man. When confronting him, the superheroes are affected in equally slapstick ways, such as enlarging the Flash's feet so he can't run, or sticking Wildcat to Batman's back. They're able to fight back despite their transformations, but can't defeat the indefatigable and silent Anti-Matter Man.
The Atom ends up saving the day by miniaturizing and then expanding the Spectre, resulting in an explosion that blows the Earths back to their native dimensions as well as the Anti-Matter Man.