Detective Alex Cruz is a former gang member turned police officer for the LAPD.
Alejandro "Alex" Cruz is an ex-gang member, who used to run with the "Loco's," one of LA's most dangerous gangs. Now, he is reformed and now gets business taken care of in the LAPD, when kicking down doors in the Gang and Narcotics division.
Though a tad green and brash, Detectives Riggs and Murtaugh see past Cruz’s tattoos and hard demeanor and recruit him into the Robbery/Homicide division where he quickly becomes an intrinsic addition to the team. He is often seen with Bailey, who he's partnered up with.
Judging from Cruz's hard demeanor, he used to be a serious gang member of the Loco's, and his tattoos he has are what remind him of his past and how he's able to do well in serving the community and committed to doing so. Now, reformed, he makes up for the past by helping out the community and protecting it by joining the police force. When it comes to getting business taken care of, he means business, especially when kicking down doors and busting gang members and drug dealers in the Gang and Narcotics Division, or even the Robbery/Homicide division.
According to the Internet Movie Database, and Wikipedia, Richard Cabral, who plays Cruz, did actually used to be in a gang once, coincidentally like Cruz used to, prior to his acting career. He obtained his GED as a teenager, but once again got in trouble with the law. He was sentenced to prison for violent assault with a deadly weapon; he was released at the age of 25.