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Good to see you're still working on these. It's worth noting that matrix multiplication in general requires the left matrix to have as many columns as the right matrix has rows. I have a doubt about the equation î * î + ĵ * ĵ = 1. Since a vector dotted by itself gives the length, and these are both unit vectors, shouldn't the sum be 2?
Thank you for fact checking. I'm aware of matrix dimensions for multiplication, but this section is only meant to be introductory for two-dimensional use. I needed it to effectively demonstrate conic rotations and still have to add operations with both vectors and matrices. In 3D, they will be fully covered. I do have to point out why there is an intuitive difference between a scalar matrix and scalar multiplication.
You are right about the dot product. That is actually supposed to be an equals instead of a plus, so I erred.