The interesting thing about C is when you do this operation:
For the example matrix I gave A, this gives:
The sum of all of these entries is exactly the same as the sum of all the entries in matrix A!
If you look at matrix A and the resultant matrix you can see that every cell gets closer to the average value of all the entries in the matrix, which is what you would expect from a grid of temperatures settling into an average temperature.
Let's look at the bottom right cell in A, that starts off at 7 and goes to 4.875, another application of the matrix multiplication with C gives:
You can see it is is sort of exponentially decaying to the average temperature of 3.444