Kronecker delta

I'm beginning to get my head round the way that matrices can be written by setting out individual elements within them rather than by writing out the matrix itself. I now realise that when matrices can approach infinitely big sets, then it's just not possible to write them out. In matrix maths, the identity matrix I acts like the number 1 in ordinary arithmetic. I is a diagonal matrix with 1 down the diagonal and 0 everywhere else. So when we don't want to draw matrix, the Kronecker delta symbol is helpful. It = 1 when i=j (so any place that would be on the diagonal of a matrix) but 0 when i and j are not the same numerical value. Sources make it clear that the Kronecker delta is not a matrix but where I see it used, it enables things to be done with individual matrix elements that would require the identity matrix in matrix maths.