What is the geometry behind the matrix multiplication?
The questions that I am having is the follows.
$\bullet$ I accept that we are viewing $\mathbb R^4$ as either in $\begin{pmatrix} a_{11},a_{12},a_{13},a_{14}\end{pmatrix}$ or $\begin{pmatrix} a_{11}&a_{12}\\a_{13}&a_{14}\end{pmatrix}$.
so, matrix addition makes sense that it gives another vector in that space.
$\bullet$ But, Matrix multiplication does not convince me in this role.
I strucked with,
Like in the matrix addition, (addition of two vectors is nothing but the diagonal of the parallelogram in which the two vectors are adjustcent sides)
is there any vector space diagramatic representation for matrix multiplication??
Note:
I am aiming to teach this factacy to my grade 11 students who are studying their matrices now only.(Means to say, this is the first time they gonna meet matrices)
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