Question

What are some sample matrix multiplication problems?

Answer 1

It doesn't commute, or is not always defined.

Explanation:

The product of two square matrices (a square matrix is a matrix that has the same number of rows and columns) `AB` is not always equal to `BA`. Try it with `A = ((0,1),(0,0))` and `B =((0,0),(0,1))`.

In order to calculate the product of two rectangular matrices `C` and `D`, if you want `CD` you need `C` to have the same number of columns as the number of rows of `D`. If you want `DC` it's the same problem with the number of columns of `D` and the number of lines of `C`.