McRae allegedly shot eight people at Michigan State University, killing three, Monday evening.
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WATCH: Authorities ID Michigan State shooter
Authorities ID MSU shooter
McRae died of a self-inflicted gunshot wound as law enforcement was approaching, a law enforcement source briefed on the situation told ABC News. The source added that a firearm was recovered at the scene, and a second firearm was found in backpack along with numerous magazines.
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McRae served 18 months in prison between 2019 and 2021 on a weapons charge for having a loaded weapon in his vehicle, according to the state's Department of Corrections. The offense took place in Ingham County, which covers East Lansing. He is listed on the DOC site as a 5' 4" male.
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Law enforcement is combing through his social media and writings for any extremist views, including for misogyny, satanic musings, signs of isolation, and possible conspiracy theories, sources said.
In a confidential briefing to law enforcement Tuesday, the FBI said it has determined McRae walked from his home to the school and had no connection either to the university or the victims.
They said the gunman had psychiatric issues and, when he was found, had a "3-page document expressing his reasons for the attack and a number of additional locations in Lansing and Holt, Mich.; Ewing Township and Franklin Park, NJ; and Colorado Springs, Colo., which had 'hurted' (sic) him and, therefore, were deserving of attack."
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Agents believe "personal grievances" with people at those locations are the reasons why they were mentioned in the writing.
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The briefing said the "subject claimed in his letter that he is the leader of a group who would pursue his agenda on his behalf... the FBI has yet to gather information confirming any threat to the listed locations or involvement from other parties."
Investigators reported that the suspect's writings confirmed "the deceased was often alone." The briefing said the gunman viewed himself as "a loner" and an "outcast" who was "never noticed or accepted by others."
The shooter lived with his father, who is cooperating with the investigation, the FBI reported.
In addition to motive, detectives are actively trying to determine what led the shooter to attack that specific location on the MSU campus.
ABC News contributed to this report.