Why can we multiply matrices, but not coordinates? – math.stackexchange.com

LayOfTheLaw121
In my studies of linear algebra, I learned that the identity matrix $$I = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}$$ is just basically the number $1$ ...