A note on matrix multiplication appearing as element concatenation or coinciding with matrix addition.

In this note we demonstrate two instances where matrix multiplication can be easily verified. In the first setting, the matrix product appears as matrix element concatenation, and in the second, the product coincides with matrix addition. General proofs for some results are provided with a more complete description for $ 2 \times 2 $ 2 × 2 matrices. Suggested for consolidation of the algorithm rather than as an introduction, we believe the example base that can be created, combined with an analysis for understanding the context, acts as a positive motivator to secure mastery as it needs to be practised. [ABSTRACT FROM AUTHOR]