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 2×2 matrices. Suggested for…

Traditionally, learning basic facts has focused on rote memorization of isolated facts, typically through the use of flash cards, repeated drilling, and timed testing. However, as many experienced teachers have seen, "drill alone does not develop mastery of single-digit combinations." In contrast, a fluency approach to learning basic addition…