asalam walaikum, my sibling tends to walk around the house without slippers even toilet, i have asked her to wear it but she rejects,just worried if carpet is napak, not sure if the prayer mat is napak too as although it is dry i did wudu and my feet are wet and not sure whetether it has transfered on my clothes and the mat. thanks.
Beware you are rapidly becoming a doubtful person soon to become paranoid. When you are absolutely certain something is definitely na-paak then only regard it so, otherwise you will go crazy.