Comments by "Liam" (@1495978707) on "Matrix multiplication as composition | Chapter 4, Essence of linear algebra" video.

I was just thinking at around 9:30 that that way of thinking about it does seem like cheating, like it's not a rigorous proof because it wasn't filled with mathematical notation and convoluted. Just saying "well it's clearly true" doesn't feel sufficient, but it's a gut/intuitive feeling, and that's what is most helpful in this endeavor. This is often an issue I have with physics homeworks that I have; I understand concepts intuitively very quickly and that allows me to skip a lot of hard messy work but it leaves me feeling guilty because it doesn't seem rigorous enough, even though I clearly had to understand it to make those jumps. Thankfully in higher level physics classes with handwritten homework this generally isn't an issue for the exact reason that it's better if I can figure it out without slaving over it, I just have to prove that I'm not cheating and am genuinely figuring it out for myself. That's my 2 cents.
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