## Precalculus (6th Edition) Blitzer

Consider the matrix given below: $A=\left[ \begin{matrix} {{a}_{11}} & {{a}_{12}} \\ {{a}_{21}} & {{a}_{22}} \\ \end{matrix} \right]$ Then \begin{align} & -4A=-4\left[ \begin{matrix} {{a}_{11}} & {{a}_{12}} \\ {{a}_{21}} & {{a}_{22}} \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} -4{{a}_{11}} & -4{{a}_{12}} \\ -4{{a}_{21}} & -4{{a}_{22}} \\ \end{matrix} \right] \end{align} We see that $-4A$ is obtained by multiplying each element of $A$ by $-4$. Therefore, the given statement is true.