What Should a Matriarchal Society Look Like?

by bdhesse

In one of the stories I’m currently working on, my protagonist discovers a matriarchal society. This has got me wondering: what should a matriarchal society in fiction look like? Very few stories have such societies, but most of the time they are either Amazons or Amazonian-like. So, given the opportunity to write a matriarchal society, what would it look like?