It's more complex to frame it as matriarchy or patriarchy. There are aspects of both at play, just as the area that became Vietnam was an interaction zone between different cultures. So, Keith Taylor notes that it's possible that the Trung Sisters rebellion originated with a dispute over inheritance rights. In Chinese society at this time, wealth was inherited by men through their fathers. But among the Lac (the ethnic group living in what is today Vietnam), men and women inherited wealth through their mothers. There was a practice of 'levirate' practiced too by the Lac. This allowed widows without children to procreate with her in-laws, with the male relatives of her dead husband. This would give her the opportunity to produce an heir! This was not practiced in Chinese society. But this could also be used to produce an heir for the dead husband.

Now, recall that these details were written much later. The Chinese records say, according to Taylor, that circa 43CE one Lac lord was "tied up with the law." This lord was married to two women, the Trung sisters, who were daughters of another Lac lord (the whole marriage arranged by their father doesn't go along with our idea today of matriarchy). Taylor writes that it's possible his being "tied up with the law" could mean he was trying to enable his wives to inherit the wealth/property of their father, the other Lac lord. So there's a possibility of matriarchal means used for patriarchal ends... But matriarchal inheritance contravened Chinese administrative law. The husband was executed by Chinese administrators in the ensuing dispute.

The sisters ruled for two years. The Chinese only noted that their reign was marked with "adjusted taxes".

Generally though the Chinese style laws and social/patriarchal customs grew after this period in tandem with Chinese administrative rule. By the 15th century, it was unthinkable to Vietnamese that their ancient ancestors had potentially lived in a matrilocal society (where husbands live with their wives' family).

It used to be argued that under the Le and Mac dynasties (15th to 18th century) the legal code was more favorable to women and allowed matrilineal inheritances. This was used in nationalist arguments about Vietnamese being 'distinct' from China or by regional area studies scholars who wanted to assert Vietnam was part of a matrilineal Southeast Asian culture rather than a patriarchal East Asia. But in practice, elites in Vietnam actually emulated Chinese cultural and social practices by and large, trying to become 'van hien' or civil -- which was to say become more Chinese-like.

On women in particular, Nhung Tran shows that in practice under the Le code women did not enjoy the freedom to allocate their inheritances. The Le code and local legal regulations maintained, in practice, the allocation of inheritance to male heirs. Instead, women found they would distribute their resources/land to local institutions, often religious, prior to death, to assert control over their destination. This allowed them to attain status and to perpetuate their ancestral cult.

So, in sum, it's not an all-or-nothing prospect. There were matriarchal aspects and patriarchal aspects that intertwined, without a clear era.

Keith Taylor, A History of the Vietnamese (Cambridge, 2012), 21-22, 15.

Nhung Tran, "Gender, Property, and the "Autonomy Thesis" in Southeast Asia: The Endowment of Local Succession in Early Modern Vietnam," The Journal of Asian Studies Vol. 67, No. 1 (Feb., 2008), pp. 43-72.