Multiplication of a matrix by a scalar simply means multiplying a matrix by a fixed constant. We saw (or will see, depending on if you got there or not yet) that matrices can be added together by simply adding up the corresponding elements in the grids. 


If the matrices were identical we would have a situation such as A + A = 2A. In this case we could simply take matrix A and multiply it by the scalar 2. Here is an example:



As you can see, the result is the multiplication of each element by the scalar, resulting in the product matrix.