A matrix can be multiplied by a number. To consider this, addition of matrices will be used.

Consider the matrix A, 3x2

```   / a  d \
A=|  b  e  |
\ c  f /
```
Adding A to itself, or computing the sum A+A yeilds:
```     / a  d \     / a  d \     / a+a  d+d \     / 2a  2d \
A+A=|  b  e  | + |  b  e  | = |  b+b  e+e  | = |  2b  2e  |
\ c  f /     \ c  f /     \ c+c  f+f /     \ 2c  2f /
```
Thus, the sum A+A, or 2A is twice the original matrix.
```              / a  d \     / 2a  2d \
A+A = 2A = 2 |  b  e  | = |  2b  2e  |
\ c  f /     \ 2c  2f /
```

It follows that in order to multiply a matrix by a number, simply multiply each element in the matrix by the number by which the matrix is being multiplied.

It should also be noted that the order in which to write a matrix multiplied by a number is with the number first, appearing directly to the left side of the matrix.

In summary:

```      / αa  αd \
αA = |  αb  αe  |
\ αc  αf /
```

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