# 2.3 Scalar Multiplication

The product of an m × n matrix A and a scalar $\alpha$ is an m × n matrix whose elements are the arithmetic products of $\alpha$ and the elements of A.

 $\mathbf{C}=\alpha\cdot\mathbf{A}$ (7)

implies

 $c_{ij}=\alpha\cdot{a}_{ij},\operatorname{where}1\leq i\leq m\operatorname{and}% 1\leq j\leq n$ (8)