Product Yields I

It is clear that (2I)(0.5I) = 2 (0.5)I = 1I = I. But, just for practice, mentally multiply out these matrices the long way:

2 0 0 0 2 0 0 0 2

1/2 0 0 0 1/2 0 0 0 1/2

The rows from the first matrix "match" the columns of the second so that the dot product is 1 only for the major diagonal. All other dot products are 0. The resulting matrix is I.