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

Abstract

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 $2\times 2$ 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.

Keywords:

• Matrix multiplication
• concatenation
• matrix addition

2020 Mathematics Subject Classification:

• 15A24

Acknowledgments

We thank the reviewers for their comments which added to the clarity and readability, resulting in the work being better embedded in the literature.

Disclosure statement

No potential conflict of interest was reported by the authors.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.