Suppose that $A$ is an $m\times n$ matrix and $B$ is an $n\times p$ matrix. Prove that the column space of $AB$ is a subset of the column space of $A$, that is $\csp{AB}\subseteq\csp{A}$. Provide an example where the opposite is false, in other words give an example where $\csp{A}\not\subseteq\csp{AB}$. (Compare with Exercise MM.T40.)