need immediate help

a) Let T: V V be a linear transformation, where V is a finite dimensional vector space. If dim(range(T))=dim(range(T2)) show that the range and null space of T only have the zero vector in common.

b)

Let T: l2 (Zn)--- l2 (Zn) be a linear transformation. Show that T is translation invariant if and only if T(z) = ∑K=0N-1 ak Rk(z) for some a0 ,……,aN-1