Originally Posted by

**Deveno** i don't think that's quite right. in the first place, your initial choice for v has to be non-zero.

now, even with that proviso, span(v) is isomorphic to Zp, so it has p elements. that gives us (p^2 - 1)(p^2 - p) choices, according to you.

so in Z2 x Z2, we should have 6 possible choices of a basis:

picking (0,1) first, we could form: {(0,1), (1,0)} or {(0,1), (1,1)} as a basis (so far, so good).

picking (1,0) first, we could form: {(1,0), (0,1)} or {(1,0), (1,1)} as a basis....wait a minute. we already HAVE {(1,0), (0,1)} = {(0,1), (1,0)}

as a basis....i didn't see anything in the problem stating they should be ORDERED bases.