Scalar Multiplication of a Matrix

Multiplying a matrix by a number

When a matrix $A$ is multiplied by an ordinary number $k$ (called a scalar, to distinguish it from a matrix), every SINGLE element of $A$ is multiplied by $k$:

For example, if $A = \begin{pmatrix} 2 & -3 \\ 0 & 4 \end{pmatrix}$, then $3A = \begin{pmatrix} 6 & -9 \\ 0 & 12 \end{pmatrix}$ — every element, including the zero, is multiplied by 3.