# What is scalar multiplication of matrices?

Simply the multiplication of a scalar (generally a real number) by a matrix.

The multiplication of a matriz $M$ of entries ${m}_{i j}$ by a scalar $a$ is defined as the matrix of entries $a {m}_{i j}$ and is denoted $a M$.

Example:

Take the matrix

$A = \left(\begin{matrix}3 & 14 \\ - 4 & 2\end{matrix}\right)$

and the scalar $b = 4$

Then, the product $b A$ of the scalar $b$ and the matrix $A$ is the matrix

$b A = \left(\begin{matrix}12 & 56 \\ - 16 & 8\end{matrix}\right)$

This operation has very simple properties that are analogous to that of the real numbers.