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I'm writing a fantasy comic, and in my comics, I plan to introduce a country/nation/race, where women dominate everything. Men from this race/nation are submissive to the women. Women have all the Authority. Women go to war. Women decide from the top. Men stay home and take care of the babies. It's like a roles reversed country based on the old ways. Would a country like that work? And how would it work?

EDIT: I may have phrased my question wrongly. I'm talking about a fantasy human race where women have 100% domination over the men. There's semi-common technology(1970s Max) . Baby formulas are available. Men help procreate. They do the meager jobs. Men of this nation are genetically placid. It's an exaggerated concept. Which is why I ask if a society that men contribute little to anything significant could work.

No human society would be structured like this. Two of your points reveal why.

Women go to war.

Men are far more physically suited to combat than women. A nation that uses female warriors will be conquered by one that uses male warriors. Weapons tech doesn't help much here--men still have faster reaction times than women, can carry heavier loads, and have more endurance, which are all relevant to combat.

Men stay home and take care of the babies.

Men don't have breasts. They can't take care of babies without a woman present. So this just ends up being inefficient. Tech doesn't really help this issue, either, because social structures come first, and they tend to have quite a bit of inertia. The invention of baby formula isn't going to shunt every man into a childcare position when women have been doing it for centuries.

This doesn't rule out a societal structure where women have authority and men do not. Heck, even in a male-dominated society, most men still don't have any authority, so it wouldn't be a big change for them. Men already do a whole host of important but low-status jobs in real life, so relegating them to exclusively that is hardly out of the question. But the resulting society will not be a sex-reversed patriarchy. It just doesn't work with human physiology.

Now, if you want to go nonhuman, all bets are off. You can look to nature to find all sorts of sexual arrangements and hierarchies. There's even a species of cave-dwelling book lice where the females have penises and the males have vaginas, with a corresponding reversal in sex roles. Go nuts.

Some controversial and highly disputed theories by Marija Gimbutas suggest that very ancient human societies in Neolithic Europe were indeed matriarchal until they were overrun and conquered by the "Kurgans" from the great Steppes of eastern Europe/Ukraine. Presumably the female dominated matriarchal societies did not think in terms of defence, so were easily overrun and conquered by the male dominated, warrior, "Kurgan" society.

Another legendary matriarchal society was the "Amazons", who also lived in the Steppes north of the Black Sea according to some legends. Oddly enough, there have been Scythian grave sites from that region with female remains surrounded by weapons and armour in the same manner as high ranking male warriors.

Real Amazons in ancient Scythia

So while there is not conclusive archaeological proof of female dominated societies, there are intriguing hints that it was possible in the distant past, so there is nothing intrinsically stopping the idea, at least for a while.

A 100% reversal doesn't make sense, especially if you limit the technological level to 1970.

Woman are capable of managing families, companies and countries, but when it comes to physically hard work, it doesn't make sense to prefer women doing it.

The evolution of our species gave men stronger muscles and more testosterone (among other things), which makes them better suited for occupations like (pre-industrialized) miners, lumber jacks or warriors.

The same evolution gave women a physically weaker body and a brain that cares more about the wellbeing of infants than a male brain. That makes them better suited for social and medical care jobs.

If you except childcare and physically hard jobs from your gender swap, it is far more believable. There's no reason why a female chief physician shouldn't instruct a male nurse or why a husband shouldn't have lunch ready when his beloved wife comes home from her job. There's no reason why sexual harassment and discrimination shouldn't work the other way around. If you define physical work as inferior or undesirable in your society, putting women into management positions and high education jobs and men into labor jobs sounds like an equivalent of the lack of job opportunities women faced in the past.

Disclaimer: Please don't start a discussion about sexism and gender bias. I support equal chances for all genders and races, but the history is what it is and cannot be changed.