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 /