Yes, a constant can be regarded as a random variable having a trivial probability distribution (why not?). Don't confuse "random" with its usual meaning!

It doesn't really matter whether your are matrices or vectors. In any case matrices can be regarded as special vectors. Start from the definition of the expected value. Now how do you define the expected value of a vector? How are your vector random variables constructed? Do the coordinates of your random vector all have the same probability distribution, or do they have separate probability distributions?