Suppose that A is an m n matrix and B is an n p matrix.

Question:

Suppose that A is an m n matrix and B is an n × p matrix. Prove that the null space of B is a subset of the null space of AB, that is N(B) ⊆ N(AB). Provide an example where the opposite is false, in other words give an example where N(AB) ⊈ N(B).