Question

How to prove these question

(1)Let O denote the zero map O : R^n → R^n, and let T : R^n → R^n. Show that if T^k = O for some k, then T^n = O.

(2)Suppose T : R^n → R^k , U : R^k → R^m are linear maps. Show that nullity(U ◦ T) ≤ nullity(U) + nullity(T).