Say I have two matrices $A$ and $B$ where $A$ has dimensions of $1 \times 2$ ($1$ row, $2$ columns) and $B$ has dimensions of $2 \times 3$ ($2$ rows, $3$ columns)
When you multiply these like so $(A \cdot B)$ you get a $1 \times 3$ matrix.
It was my understanding that this was correct, but I was advised by a grader that I should have done it like so, where $A$ as a $2 \times 1$ matrix and $B$ as a $3 \times 2$ matrix
Then, when multiplying do it like so $(B \cdot A)$ which gives a $3 \times 1$ matrix.
Both approaches give the same three numbers, except one is a $3 \times 1$ matrix and the other a $1 \times 3$.
It was my belief that both were correct and which one you chose is arbitrary. Have I misunderstood?
Additionally, the matrices were intended to reflect the weights on a graph in a figure. Should the presentation of such a graph effect how I decide to represent their dimensions as matrices? Again, I didn't think this was the case...