Are Female Heads of Households a Problem in the First Century?

In the Greco-Roman environment, given everything we know about male and female relationships in the first century, would a single female homeowner be viewed as the de facto leader over men? Some of them would have been male heads of household. Maybe they would have had higher status than her even. And all that comes with it, which I think would at least raise questions about whether a single woman would be exercising authority over another woman's husband.