Suppose that there are some $n$ matrices, $A_1, A_2, ..., A_n$ One wants to form a square matrix $B$ that contains all aforementioned $A$ matrices as entries (this does not mean that all components of the matrix $B$ must be $A$ matrices, though.). One wants to do the following: 1) When multiplying $B$ matrix by itself, one wants to see the result of multiplication that has entries of the form $A_i \times A_j$. How would I achieve this?
2) not related to 1): Suppose that we multiply $B$ by some matrix $C$. Again, one wants to see the result of multiplication that has entries of the form $A_i \times A_j$. How would I achieve this?