Assume matrices $A$, $B$, and $C$ are of same dimensions, does $\|A\|\_2\leq \|B\|\_2$ imply $\|CA\|\_2\leq \|CB\|\_2$ or $\|AC\|\_2\leq \|BC\|\_2$? 

$\|A\|\_2$ denotes by $\lambda\_{max}\sqrt{A^TA}$, and $\lambda\_{max}$ is the largest eigenvalue.