'matriarchally' originates from 'English', specifically the word 'matriarchal', where 'matriarch' meant 'a woman who is the head of a family or tribe' and the suffix '-ly' forms an adverb.

'matriarchally' changed from the English word 'matriarchal' (adjective) by adding the adverbial suffix '-ly', and eventually became the modern English word 'matriarchally'.

Initially, it meant 'in a manner relating to a matriarch or matriarchy', and this meaning has remained consistent in modern usage.