We call this for short, the so called "Kronecker delta".

Let's just calculate what the element in the i-th row and k-th column will be for the two cases:Show that AI = IA = A for every n x n matrix A.

Once again I know that this statement is true as I know what the identity matrix is and when I use the identity matrix I understand why this works, but I am unsure how I would clearly show this. Any help is greatly appreciated. Thank you very much!

by definition of , since for all we have .

and, similarly,

, by definition of

So what we have shown that and , and thus .