Relevant Wikipedia article:

"Penny Farthing" bicycle race at Herne Hill (1937)
GAUMONT BRITISH NEWSREEL (REUTERS)To license this film, visit https://www.britishpathe.com/video/VLVA9C8BQGVH0UZ9OAMI7CVJYKFGY-PENNY-FARTHING-BICYCLE-RACE-AT...
Relevant Wikipedia article:
If anything, it is more standard to put a brake on the front wheel. (?)
One guy told me about his rear-wheel braking technique of lifting the rear wheel momentarily off the ground and stopping its rotation using the pedals, so that the resulting friction slows down the bicycle when the rear wheel re-contacts the road.
NB those 1880s bicycle catalogues are on the Internet Archive, and they list every type of bicycle and what standard equipment it came with. In 1881 safety bicycles were still classified as “peculiar” — an ordinary bicycle was a penny-farthing — but just a few years later they had their own dedicated section. Going through it you can see details on dozens of models.
I’m not sure if you meant “put brakes on the rear wheel” or “butt brake” (as in sit your ass on the wheel to slow it down). Both are possible, although the former is probably more comfortable.
If anything, it is more standard to put a brake on the front wheel. (?)
What I’m familiar with is putting a caliper brake on one wheel to take pressure of the legs when trying to stop a fixie. Honestly, my memory is failing me on whether they were on the front or rear. Front has more braking power but in my mind I’d be worried about flipping the bike. Real fixie riders probably have better control than me.
This 1937 film captures a bicycle race featuring both the then-modern bikes and the classic “Penny Farthing” models. The older Penny Farthings, even when ridden by older gents, managed to reach impressive speeds.

GAUMONT BRITISH NEWSREEL (REUTERS)To license this film, visit https://www.britishpathe.com/video/VLVA9C8BQGVH0UZ9OAMI7CVJYKFGY-PENNY-FARTHING-BICYCLE-RACE-AT...
I’ve never ridden a bike that couldn’t coast.
My first bicycle had a rear brake that was engaged by pedaling backwards. So did the rest of my childhood bicycles.
I had an “intermediate” bicycle that had a rear pedal brake and a front caliper hand brake.
My adult bicycles all had just caliper hand brakes.
I’ve never ridden a bike that couldn’t coast.
That’s why fixies are so cool.
Note that bikes used in velodrome racing are also fixed gear.
The idea behind braking a fixed gear bike isn’t to get the pedals to turn backwards but to apply reverse pressure to get them to turn more slowly. So not like how you use coaster brakes.
Thanks, all, for not nitpicking the typo in the first word of my title (obviously, I was thinking ahead to the parenthetical “was?” but trying t type “What”) and for all the helpful knowledge here. It’s pretty amazing, the correctable errors in design that get worked out as various devices such as bikes develop.
Note that on a fixed wheel bike, you have to stop to go around a sharp corner – you can’t lift the inside foot pedal and coast around the corner, so if you take a corner, your inside pedal will bottom out and throw you off the bike.
Hence the classic use of fixies as NYC bicycle couriers: lift and throw a wheel (either front or back) to make a sharp turn through traffic or around a pedestrian or obstruction. If you’ve got a front-wheel brake, you can use that to lift the back wheel, but if not, any really good rider would be able to lift and throw just by shifting weight.