matriarchy n.

"mother or woman who heads a family or tribe," c. 1600, from matri- "mother, woman" + -arch, abstracted from patriarch, ultimately from Greek arkhein "to rule" (see archon).

suffix indicating state, condition, or quality; also activity or the result of it (as in victory, history, etc.), via Anglo-French and Old French -é, from Latin -ia, Greek -ia, from PIE *-a-, suffix forming abstract or collective nouns. It is etymologically identical with -ia and the second element in -cy, -ery, -logy, etc.