Iggy Azalea Breaks Up With Nick Young ... I Can't Trust Him

Iggy Azalea and Nick Young are done ... engagement off ... broken up ... for good.

Iggy took to social media to announce the breakup ... saying, "Unfortunately although I love Nick and have tried and tried to rebuild trust in him - It's become apparent in the last few weeks that I'm unable to."

Of course, Young was secretly recorded on video a few months back by Lakers teammate D'Angelo Russell seemingly admitting to cheating on Azalea.

At the time, Azalea said she was furious ... but decided to give Young one last chance.

FYI -- the two have dated for several years ... and were engaged to be married.