I have an arbitrary diagonal matrix D and an arbitrary matrix A. I want to show that the jth column of the product AD is equal to the jth diagonal entry multiplied by the jth column of A.
My idea here is to take D and partition it in such a way that I capture the said jth component in a 1x1 matrix... and then I want to take A and partition it into generic columns... in which I would get the jth component to multiply all the columns I need to figure out how to isolate only the jth column of A I can do that...but I don't want to fall into a logical trap or just fall into a trap where I am reducing the problem unnecessarily so am I going down a good road or bad road any suggestions will help
It seems to me that you are making the problem more difficult than it needs to be. If I were you I would go directly to the definition of matrix multiplication: $$(AB)_{i,j} = \sum_{k=1}^n A_{i,k}B_{k,j}$$ This should hopefully lead you in the right direction.