Answer
The product of a matrix with a scalar number is defined as multiplication of that scalar with each element in the matrix.
Work Step by Step
The product of a matrix with a scalar number is defined as multiplication of that scalar with each element in the matrix, that is, if a matrix $A={{\left[ {{a}_{ij}} \right]}_{m\times n}}$, then multiplication with scalar k is as follows:
$kA={{\left[ k{{a}_{ij}} \right]}_{m\times n}}$.
Consider the $2\times 2$ matrix $\left( \begin{matrix}
a & b \\
c & d \\
\end{matrix} \right)$ and a scalar k:
$k\left( \begin{matrix}
a & b \\
c & d \\
\end{matrix} \right)=\left( \begin{matrix}
ka & kb \\
kc & kd \\
\end{matrix} \right)$
Example:
Consider the following matrix:
$A=\left[ \begin{matrix}
3 & -9 \\
5 & 4 \\
\end{matrix} \right]$
To obtain the product of -2 and A, compute as follows:
$-2\left( A \right)=-2\left[ \begin{matrix}
3 & -9 \\
5 & 4 \\
\end{matrix} \right]$
$\begin{align}
& -2\left( A \right)=\left[ \begin{matrix}
3\left( -2 \right) & -9\left( -2 \right) \\
5\left( -2 \right) & 4\left( -2 \right) \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
-6 & 18 \\
-10 & -8 \\
\end{matrix} \right]
\end{align}$
Therefore, the product of -2 and A is $-2A=\left[ \begin{matrix}
-6 & 18 \\
-10 & -8 \\
\end{matrix} \right]$.
