Note that this transaction is considered by the IRS to be part gift/part sale. As such your basis in the property will be the greater of your sibling's basis in the property or the amount paid by you to buyout your sibling's share ($200,000).
See https://www.law.cornell.edu/cfr/text/26/1.1015-4
Generally, your basis and your sibling's basis would be the fair market value on the date of death of your mother (e.g., $500,000 each).
I am sorry for your loss.
