You're right Presentjoy, that there is a difference between matriarchal and matrilineal societies, and that the latter can be partriarchal. I'm Jewish, and we are an example.
It's been my experience that there is a lot of confusion about the word matriarchy. Many think that it describes a society where only women rule, rather than men and women equally. Matriarchies are egalitarian, though. Some Native American tribes are examples. (It's funny to note that Native Americans thought that the European settlers were strange because of their refusal to do business with the females of the tribe.) A matriarchy is achieved when at least half of those who rule are women. Sweden is almost there, as well as Rwanda. Matriarchy is also different from patriarchy, in that it requires no oppression of any in the group.
I can't agree with Anemone that the matriarchal societies were disorganized. Osiris wasn't introduced to Egypt as the first male god until 3000 bc. Prior to that, female goddesses were worshiped in both Upper and Lower Egypt. As early as 5500 bc, tribes had organized enough to succeed at animal husbandry and agriculture. They created works of art, jewelry, pottery, and so on. True, they lived simpler lives than the later invaders, but I am not sure that renders them disorganized. As for literacy, since the fairly recent discovery that writing started a full 500 years earlier than previously thought , we can see that the written word was around long before any male gods were even introduced.
And you guys are so right about that relic looking like a dildo!