In some ways, this obsession with matriarchy seems a little insulting today. Beloved TV characters face the horror of realizing that WOMEN ARE IN CHARGE! Why, it's terrifying...
Today, of course, that fear is just sexist, and we have seen many great female leaders around the globe. Thus far, no men have been rounded up and taken to internment camps, or made slaves to diabolical "mistresses" of totalitarian matriarchies.
The Star Trek franchise has featured matriarchies on more than one occasion. In the original series third season premiere, "Spock's Brain," the Enterprise encounters the "Eyemorgs," the women rulers of planet of Sigma Draconis VI.
In The Animated Series (1973 - 1974), The Enterprise encountered another matriarchy, one bound and determined to drain the life-force of Captain Kirk, Mr. Spock, and the entire male contingent of the Enterprise crew. Lt. Uhura (Nichelle Nichols) took command of the starship, and fought back against these sirens.
Considering the Earth a “great disappointment,” the Medusan Matriarchy sets out to retrieve Shem and Adam. If they fail, a new, illegal “men’s liberation movement” could take hold on Medusa, overturning the apple cart.
To convince these visiting men to remain docile and cooperative, this cold-hearted queen then poisons their food, and tells the men they will only receive the antidote only if they comply with her wishes.
In "Angel One," a first season episode of Star Trek: The Next Generation, the Enterprise D visits the Matriarchy of “Angel One” in hopes of finding out if survivors of a freighter, the Odin, landed there. They find out that a group of men did survive, and are making trouble for the female leadership.
Even by the 1990s, science fiction television was still trotting out this old (and now ridiculous trope). Sliders (1995 - 1999) featured an episode titled "The Weaker Sex" in 1995, wherein Quinn, Arturo, Wade and Rembrandt slide into a parallel Earth that is a matriarchy.