Show that the jth column of the matrix product AB is equal to the matrix product ABj, where Bj is the jth column of B.
I know this is true, but I'm not sure how to show it. Could someone please help me out? TIA!!!
I would consider this to be more of a definition than something that needs to be proved.
Let $\displaystyle [A_{ij}]$ and $\displaystyle [B_{jk}]$ be your matrices.
Then by the definition of matrix multiplication:
$\displaystyle C_{mn} \equiv \sum_{j} A_{mj}B_{jn}$
So the jth column vector in C is $\displaystyle C_j = AB_j$ by definition.
-Dan