Actually, I made the term I used "matrilineal" (children know who the mother is, father not really in the picture) rather than "matriarchal" (women rule) for a reason.
Look at matrilineal societies like Somalia or South-Central LA. The women don't rule. Nobody really rules, builds, or establishes anything. You just have competing gangs of men, and the women are effectively owned by whichever man chooses to offer them temporary protection from the other predatory males, or they're on their own.
I've never seen a historical record of a true matriarchal society (as distinct from a patriarchal society that happens to have a woman succeed to the throne every once in a while)
I haven't either because I think it's like you imply ---women only have equal power in a patriarchal society, the matrilineal societies, they are impoverished and raising children alone or temporarily with serial boyfriends or the government sends a check.