The Mosuo are _matrilineal_ (figure out which kinship group you're in based on Mom's line) but not _matriarchal_ (women hold most of the political power).

You'll occasionally see it argued that the Mosuo are matriarchal, but what's going on is many people are desperate to try to find an example of matriarchy, and the Mosuo are as close as it gets. So yeah, if you squint, stand on one leg, and crook your head a bit it sort of looks like they might be.

What's really the case is that every single human society we know of has been some flavor of patriarchal.