I agree with Stoid. *Matriarchal[/i ]would be “women rule”, men structurally subordinated to women, etc., and there’s no reason to think such a system has ever existed.
Some theorists (e.g., Fisher, French) believe there may have been a time when society was matrifocal and matrilineal, although there’s so substantive supportive evidence. Most “matrifocal” stuff pertains to religion, the idea that theological God and Creator images were female (God gave birth to the universe and she is our Mother, etc). “Matrilineal” pertains to how family relationships were traced, the idea that people were known as “FirstName, the child of Mother” and that if there was a corollary to the modern LastName it would have been passed down on the maternal line rather than the paternal line.
Some theorists in contrast (e.g., Dinnerstein, Janeway) believe there has never been an actual time period of female centrality like that, but that for each individual, psychologically, there is a mental and emotional memory of such a time (their own childhood, of course, in a world where child-raising has been a predominantly female activity), and that this child-memory of Almighty Mother has a lot to do with the emotional fervor with which some people fear women possessing power or perceive women as having more political and social power than they actually have.