My view is that the people who get to matrix algebra didn&#x27;t have problem understanding the random seeming operation of previous math courses. Consider the existence of the &quot;FOIL&quot; mnemonic for multiplying two binomials (<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;FOIL_method" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;FOIL_method</a> ), or SOH-CAH-TOA, where it was easier for me to just remember the definitions than the acronym. I think those are hints that some people consider those to be &#x27;random seeming&#x27;.<p>When I took algebra, I remember being tripped by all the new vocabulary. Why do mathematicians say something is &quot;Abelian&quot; instead of &#x27;commutative&#x27;? Why is it important to have terms like &quot;group&quot;, &quot;ring&quot;, and &quot;vector space&quot;? Sure, I learned the definitions, but at that level they were &#x27;random seeming&#x27;.