Who is a good representation of a matriarch and patriarch in ancient mythology?
In general, female goddesses are potentially matriarchal and male gods patriarchs. More specifically, a patriarch is a powerful male head of a family and a matriarch a powerful female mother figure.
In ancient Greek mythology, it appears that there was an earlier matriarchal pre-Greek substrate, later replaced by a more patriarchal group of deities. The evidence of this lies in the stories of the Olympian gods overthrowing their predecessors.
Gaia was the original goddess of the earth, who acted as the mother of the other gods and creator of the world. She is probably a remnant of an earlier matriarchal religion. Zeus, on the other hand, is a typical patriarchal Indo-European sky god, and ruler of the Olympian deities.
Hesiod's Theogony is a good source for the history of the Greek gods and the Olympian overthrow of the Titans. The Furies, who have a prominent role in Aeschylus' Eumenides are also a remnant of an earlier matriarchal system of religion.