Open Question: Does a "living Interest" need to be documented? and if so where?

My mother gifted my brother and I her 2nd home, so our names are on the title. I know we verbally agreed to let her use the property whenever she wanted, and she was the one using it most. I don’t believe that was written anywhere however.
Now she has passed away, and my brother wants to buy me out of my half. Must I base taxes on the sale from when my mother inherited the property, or if she had a “living interest”, it would be from the current value and there for no tax.
Does the agreement need to be in writing somewhere? And what would we need for probate which her assets are going through now?
Thank you very much.
Sincerely,
Jane
I am talking about taxes…they are based on the difference between the value of the property when my mother inherited it, and what it is worth now. If my mother had a “living interest” in the property, then the taxes would be based from the current value, not back when my mother got the property.