Section 3.2 Scalar Multiplication
A matrix can be multiplied by a scalar, in which case each element of the matrix is multiplied by the scalar. In components,
\begin{equation}
C_{ij}=\lambda A_{ij}\tag{3.2.1}
\end{equation}
where \(\lambda\) is a scalar, that is, a complex number. For example, if
\begin{equation}
A = \left(\begin{array}{cc}
a\amp b\\
c\amp d
\end{array} \right)\text{,}\tag{3.2.2}
\end{equation}
then
\begin{equation}
3A=3\cdot \left(\begin{array}{cc}
a\amp b\\
c\amp d
\end{array} \right)
= \left(\begin{array}{cc}
3a\amp 3b\\
3c\amp 3d
\end{array} \right)\text{.}\tag{3.2.3}
\end{equation}
Try it for yourself by computing
\begin{equation}
i\cdot \left(\begin{array}{cc}
1\amp i\\
-2i\amp 3
\end{array} \right)\text{.}\tag{3.2.4}
\end{equation}