General Matthew Shrieve was a corrupt general of the U.S. Army. Fearing China would eventually bring the end of America, Shrieve plotted China's downfall with a bio-weapon which killed thousands in Hong Kong including Akio Yamashiro. In rage, Shrieve was executed by Akio's father, Maseo, but only after hours of painful torture by Oliver Queen.
After Oliver Queen stopped Chien Na Wei from selling the Omega, General Shrieve told Oliver he had to return to China for a debrief, in return, he would allow Oliver to go wherever he wished. Upon finalizing Oliver's debrief, Shrieve kept his word and allowed Oliver to go anywhere he wished, but he had to go to Japan with the Yamashiro's first. It later was revealed that he broke his promise and ordered men to hunt down and kill Oliver and the Yamashiros. It turns out, while Oliver is infiltrating an A.R.G.U.S. field house, General Shrieve had held Amanda Waller prisoner. He thought that Hong Kong was a military threat and was planning on using the Omega to destroy the city.
After Akio was subjected to the virus, Maseo and Oliver tracked down Shrieve where they forced him to procure the cure for Akio. Unfortunately there was never a cure, as Shrieve revealed that Maseo had in fact took insulin for Shrieve's diabetes. Upon his trickery, he subdued Oliver with snipers.
Due to Akio's death caused by the virus, Oliver tortured Shrieve for hours and left him unconsious until Maseo shot him in the head, killing him instantly.
Matthew was shown at first to be a man of honor, letting Oliver and the Yamashiro's go once their business was done. Matthew also at first shown to have good morals as he removed Amanda Waller's authority as the leader of A.R.G.U.S. for committing unspeakable acts. But he later revealed himself as a manipulative liar, sending men to kill Oliver and Maseo's family. He also held Amanda hostage and likely tortured her. He is probably as sociopathic and immoral as she is, if not worse, in his pursuit of his goal to wipe out China that he believes to be a major military threat using the Alpha/Omega viruses that would kill thousands of innocent people.