1. High-dimensional matrix multiplication

Given two 3*3 matrices A and B, each of which is also a vector field, that is,
each entry of A or B is a vector. For example,

A= $\begin{bmatrix} (1,2) & (1,3) & (2,5) \\ (2,2) & (3,2) & (4,2) \\ (2,4) & (2,1) & (3,5) \end{bmatrix}$

Does anybody know how to calculate the multiplication of A and B?

Thanks!

2. I would have thought you would use a normal matrix multiplication as you would with scalar entries. except with vectors there is no straight forward multiplication defined - only cross product (only in R^3) - and scalar product, which is definately more likely if it's not specified.