What can you do to prevent a 92 year old from not climbing up ladders?

I think you can try taking the ladder, maybe your should, make the house as safe as possible, but the reality with old stubborn folks is, stuff is going to happen. She can have 24/7 care or be in assited living and have a bad fall when the aid looks away for a second.

As I started dealing with my Dads dementia I was obsessed about every detail. I did everything I could think of around the house and then sit and worry that I forgot this and should have done that. I was driving myself nuts.

It's as good as I can get it, much better than most oldster homes, but one of them will fall, there'll be a trip to the e ward soon, Dads dementia is going to get worse etc. I still worry but accepting the realities of eldercare has made my life easier.

I was remembering what my mother would yell at me when I climbed trees when I was a kid: "Get down! You're going to fall and break your neck." I wonder if that would work on our parents. :)

Your mother is trying to assure herself she's still as strong and viable as she used to be. Some people who have been very self sufficient all their lives need to do this.

She probably won't change until she falls. Sad reality, but that's been my experience. The delusion of invincibility sometimes sets in as age and fragility take away one's mobility, and the need to reinforce the ability to still do challenging tasks becomes stronger.

One possible way is tell her you your admire her strength, want to be more like her, and ask if you can help her do these ladder tasks so you can learn from her. Pretend you're still the DIL who can benefit from her wisdom, ask her to show you the best way to clean the high places, and ask her to let you know whenever she's going to be doing ladder work so you can observe her style and techniques. Then once you're there, ask if you can do the work and she can guide you, and critique if necessary. This does require swallowing some pride though.

It could accomplish 2 things: (1) she won't be alone and when you're there and you can do the work under her "supervision", and (2) it could (emphasize "could") in some way reinforce her need to prove she's still a viable worker.

This approach is part of the transition from being a "doer" to becoming a "manager."

My Mom would have my Dad up on ladders without a second thought, and here Dad was 94. I would get telephone calls from Dad asking me if I could come over to change a light bulb on a ceiling fan light up on a cathedral ceiling.... good grief, no... my ladder climbing days stopped years ago. I know my limits. Any bulb changing had to be a lamp on a table.

Dad still would go up those ladders. I had noticed the cathedral ceiling ceiling fan light globe was missing.... I bet Dad accidentally dropped it as his balance and eyesight weren't the best. I also recently noticed a light cover on a ceiling light in the bathroom was missing... bet it is in pieces somewhere.

Mom was in denial about Dad's age and ability to work on the honey-do lists. And Dad was afraid to tell Mom "no".

Elders are going to climb ladders no matter what is said. You just need to hold your breath and hope it is a safe landing.

There is no way to keep another person safe. The best way is to keep ahead of problems and this means visiting often and seeing problems before they happen. This way you will be able to simply take care of things before they become a problem.
Maybe there are tree branches that need cutting back so just arrive with the tools and do the job. You may get scolded for doing something the elder feels they could still accompish, but you will have prevented a possible accident and you know they won't get the ladder out and screw the limbs back on. Keep it to things that actually need doing not things that are not done your way. For example the kitchen is in bad need of a good cleaning. Now you can clean but don't rearrange the contents to your satisfaction without asking. Think of how you would feel.

Getting outside help in is also a problem but it may be easier in the beginning if it is something you no longer want to do like house cleaning. Approach it from the point of view that the helper is there for you to help you with the cleaning. Once the helper is accepted you can then back off and gradually stop doing anything. You may still need to be there but you can spend you time visiting with your loved one not cleaning the bathroom.
You will never stop a stubborn elder and I am one of them but you can go a long way by being vigilant. "Mom I am going to the big box store would you like to come along and pick up some stuff I know you don't have a membership but I can buy things and you can reimburse me or we can share some of the big packages because I know you don't need 24 toilet rolls at once" This may take care of Mom driving to the supermarket across town when you would rather she did not drive in heavy traffic.

My dH rides his bike, there is padding in the bicycle shorts to varying degrees.
If they are going to fall anyway...
I know that getting them to wear them is impossible.

So here is my real answer:
Make sure the chores requiring a ladder are already done on a regular basis. Just think....her house will be cleaner than yours in the high places.

If they are climbing up anyway, and won't allow you to do it, stand by, holding the ladder.
At least you can call 911.

If they climb while you are not there, remove the ladder. Get a safety step stool that has wide platforms, but they cannot climb as high. You are exactly right to place things more accessible.

Jessebelle, that is exactly what I said to my neighbor, as she hangs the bird feeder higher on the tree.   And No, it didn't work so I stood by to hold the ladder. It was placed one side on a tree trunk.

Does she just forget, or is she stubbornly insisting there is no problem doing this? There isn't much you can do to combat stubbornness, but if she agrees it is a bad idea you could try putting a big sign on the ladder to remind her, that way she won't go for the chair either (hopefully)

I would just try honesty. I would say that I cared about her and didn't want to see her fall and break something -- that if she broke something, she might not be able to heal well again. An inch of prevention is worth a pound of cure. Tell her to just write down what she sees that needs to be done and you'll make sure it's done soon as possible. Let her know you're on her side when it comes to staying independent, so leave the ladder to the younger folks.

Typically, individuals are who they are when they are 10 and 90. If they are going to climb a tree at 10 they will probably do the same at 90. I'm 65 and just climbed a tree to trim some branches. No one is going to tell me I can't do it now or in ten years. My Dad was told many times not to fall (by me). He didn't listen very well because at 88 he fell and broke his hip. The main thing is that we (his children) respected his wishes to stay active and in his own home. Things happen. We all have to face our mortality at some point. Why make someone unhappy by restricting their lives and activity just to make you feel you are "keeping them safe".

I recommend a physical therapy evaluation. Ask your doctor for someone to come to her house and evaluate her or you can take her to a physical therapy office for a check up. If you get your doctor to order it, medicare will pay for it. At her age, shouldn't be a problem. Tell him you are concerned about her balance. That usually does it. Keep her safer by making sure she doesn't have any balance issues. She may have perfect balance or "good enough" balance but she may have brittle bones, so be sure to get a bone density test. If this is fine, she is in great shape which happens. Age is not the deciding factor. My aunt has home health and I just ask them to send out a therapist to check her over. They handle the doctor. I don't have to do anything but ask them to order it.
If she shows she could benefit from a round of PT or OT this can be accomplished in her home. Google senior fitness tests and you'll see some examples of things you can test for at home on your own. Test yourself first and see how you do. They have examples of what we should be able to do based on age.
She may not have balance issues or she may and doesn't realize that she does. Stand on one foot and keep your balance. Then close your eyes and do that and you'll see what I mean.
My 90 yr old aunt really benefits from the therapy and enjoys the visits with the therapists.
Have an activity planned for her when she is alone. A favorite movie, a new puzzle. Depending on her interests. Perhaps there is a neighbor who would visit with her during the time of day that she might think she needs to do these tasks. Sometimes I think boredom is the problem.
You could also put a tie on the ladder so it won't open. If she cuts the tie off, you will know she has used it. You could put a note on it with your phone number asking her to call you should she need to use the ladder. I would be inclined to remove the ladder.
Not disagreeing that she might logically get a chair but logic is not on her side and she might not think of that. It depends on where she is in her dementia. Also, she will probably forget all about it after awhile. As the disease progresses she will not want to do all of the same things.