Define Scalar multiplication of matrices?

Define Scalar multiplication of matrices?
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brawnyN
Step 1
A scalar multiplication of a matrix is defined as the multiplication of that scalar value in all entries of matrix.
Step 2
For example,
Let us consider a $3×3$ matrix with entries row wise
Now let a scalar b $\epsilon$ real number,
Matrix A define as
$A=\left(\begin{array}{ccc}{a}_{11}& {a}_{12}& {a}_{13}\\ {a}_{21}& {a}_{22}& {a}_{23}\\ {a}_{31}& {a}_{32}& {a}_{33}\end{array}\right)$
Scalar multiplication define as,
$b×A=\left(\begin{array}{ccc}b×{a}_{11}& b×{a}_{12}& b×{a}_{13}\\ b×{a}_{21}& b×{a}_{22}& b×{a}_{23}\\ b×{a}_{31}& b×{a}_{32}& b×{a}_{33}\end{array}\right)$
Jeffrey Jordon