Let V be a complex Vector Space, and a:V->V be a linear map.

a) Show that is a has finite order, then it is diagonalisable.

b) Let v in V be non-zero. Show that if there exists a smallest integer s S.T. a^s(v) = 0, then v, a(v), a^2(v),..., a^s-1(v) are Lin. Independent.

I'm really struggling with this one on a problem sheet here. Can anyone help?