Who was the gunman accused of killing four Marines in a shooting rampage Thursday at two military centers in Chattanooga, Tennessee, and why did he open fire?

Suspected shooter Mohammad Youssuf Abdulazeez, 24, is dead, the FBI said. But — publicly, at least — investigators haven’t said much more about him.

Witnesses saw Abdulazeez spray a hail of bullets at the glass doors of a military recruiting center in a strip mall. Then the gunman, who according to a law enforcement official was driving in a rented silver Ford Mustang convertible, moved on to his next target more than seven miles away: a Naval reserve center. There, he rammed into a gate at some point during his shooting rampage and was eventually killed by police, a U.S. official said.

Now, with the FBI in the lead, a terrorism task force is investigating, a law enforcement source said.

Authorities “have not determined whether it was an act of terrorism or whether it was a criminal act,” Ed Reinhold, FBI special agent in charge, told reporters. “We are looking at every possible avenue, whether it was terrorism — whether it was domestic, international — or whether it was a simple, criminal act.”

A key detail will help them make that determination: finding out the suspect’s motive.