For this case we have that by definition, object pronouns indicate who or what RECEIVES an action. Do not confuse them with subject pronouns, which indicates who or what DOES an action.
Example:
I saw you last night - Te vi anoche.
We can translate the sentence given as:
I bought the computer for my mom.
As we are referring to the third person singular, we have:
Yo compré la computadora para mi mamá. Yo se la compro.
Answer:
Yo compré la computadora para mi mamá. Yo se la compro.
