According to TMZ and their sources, it all went down at a Met Gala after party last week at the Standard Hotel in NYC.  In the video ... Jay Z, Beyonce and Solange step into the elevator ... and then Solange goes crazy, screaming at Jay before unleashing a violent attack.

As you see the fight unfold, Solange is heated about something where she begins to assault Jay Z physically while being restrained by what appears to be a body guard. Beyonce just stands there without getting involved physically; according to sources, Beyonce and Solange left together in one vehicle and Jay Z in another.