What do we know from the archaeological and historical record about societies in which women were in political authority over men (matriarchal versus matrilineal)? Herodotus et al mention "Amazons," and philosophical writers (Gimbutas et al) have speculated a great deal, but what do we really know?
You should check out the book "the Amazons" by Adrienne Mayor. The TL;DR version is that the Amazons of Greek mythology were actually scythians. We've found a bunch of warrior tombs there containing the bodies of female warriors and the descriptions of Amazons from that time period match up in terms of clothing style and stuff like that.
That being said, women fought with men but it was still a largely patriarchal society, and most of the famous Amazons from myth were probably just that: myths.