Chapter 1.7, Problem 55E

Suppose that $C$ and $B$ are $\left(2\times 2\right)$ matrices and that $B$ is singular. Show that $CB$ is singular. [Hint: By Definition 12, there is a vector ${\mathbf{x}}_1$ in $R^2$, ${\mathbf{x}}_1\ne \mathit{\theta }$, such that $B{\mathbf{x}}_1=\mathit{\theta }$.]