My mother owes back property taxes on her home and passed away I own it now do I have to pay the back property taxes

The estate, would have paid them prior to transferring ownership over to you.

*** basically you were suppose to pay them before you took ownership. But yes, if not the property could still have a lien put on it for taxes.

There is no forgiveness of property tax debt because someone dies. So if you want to keep the house, you have to pay them.