Chapter 4 - Vector Spaces - 4.9 The Rank-Nullity Theorem - True-False Review - Page 330: h

True

Obtain $(AB)x=A(Bx)$ Since $x \in nullspace (B) \rightarrow Bx=0$ then $(AB)x=0\\ \rightarrow x \in nullspace (AB)$ Hence, $nullspace (B)\subseteq nullspace (AB)$ We can say $nullity (b) \leq nullity (AB)$ Hence, the statement is true.