I agree that's a poor way to teach matrix multiplication. This topic arose last year. [0]

Don't introduce any clumsy nonstandard transformations like 'rotating' a matrix, just highlight the relevant row and column. [1]

[0] https://news.ycombinator.com/item?id=41402224

[1] https://www.mathsisfun.com/algebra/images/matrix-multiply-a.... (from https://www.mathsisfun.com/algebra/matrix-multiplying.html )

I kind of hate all these, because matrix multiplication is easiest to think of as simply repeated matrix-vector multiplication, which you need anyways (and earlier).