Hi, I need help with a linear algebra/algebra question:

Let V = (F_p)^2 = (Z/pZ)^2 [= GF(p^2)?] and K = F_p = Z/pZ where F_p is the field with p elements for some prime p

How many distinct bases for V exist?

A similar question I need help with is:

Let v_1, v_2 \in (F_p)^3\{0} such that {v_1, v_2} is linearly independent

Show that there are p^2(p-1) elements v_3 such that {v_1, v_2, v_3} is a basis of (F_p)^3

Many thanks