How to solve the problem of my mother constantly believing people are stealing from her?

Or it could something as simple as a urinary tract infection which can sometimes mimic dementia. A test for an UTI is very simple, and the doctor can either send out the results or have the lab check it if there is one in his office. There are also over-the-counter testing strips which can be found in drug stores.

54 years old is very young (but not unheard of) to be suffering from dementia. An acquaintance of mine has a mother in her early 50's with stage 3-4 dementia, so it does happen. However, there could be many other reasons for her paranoia also (chemical imbalances, psychiatric problems, etc.) that could be causing it. I agree with the others, mom has to be evaluated by a doctor who knows what is happening BEFORE hand. Call her doctor's office and explain the situation. Suggest that she be seen and evaluated WITHOUT knowing that the doctor is doing a neurological evaluation. Have them call her for an appointment for a 'routine check' or some other non-related medical problem. She will think it's their idea, not yours. (Beginning stage dementia suffers are very good at 'hiding' their mental shortcomings in front of outsiders (show-timers).
Once you've got her in there, the doc can take it from there. Hopefully s(he) will order lab tests, etc. to rule out other physical problems. If he suspects a dementia problem he can order a neurological consult, where she can be tested more in depth.

Accusations of stealing are one of the first signs of moderate dementia. It seems that everyone I've known with dementia has gone through it. I hope it's not the case for your mom. She's so young. God help your family.

Obviously this is not normal. Something is going wrong in your mother's brain. Paranoid delusions are often part of dementia, but they can be associated with other things, too.

I don't blame you for trying to reason with your mom and "prove" her delusions are wrong. That would be a natural instinct. As you discovered, it doesn't work. Delusions are very very real to the people who have them, and they just make up defenses against your reasoning (camera hacked).

Mom needs to be seen by a doctor. Make it about something other than these delusions -- she'll never agree there is anything wrong with her in that regard. Write out a list of your concerns to give to the doctor ahead of the appointment. Mother is not likely to bring this up herself.

Worrying that there might be side effects to a drug that hasn't even been suggested yet seems to me to be borrowing trouble from the future. If a drug is suggested you can research it and help Mom decide whether to take it or not. But first you need to find out what is wrong.

She needs to see a doctor. The paranoia is very early if it is dementia. There very well could be something else going on.