I’m reading a textbook about graph theory and its complications ; I just read about Incidence matrix of a graph ; one of the book’s questions which I couldn’t answer was :” What happen when we multiple an Incidence matrix with its transpose (and reverse)?”
$$I(G) I(G)^T$$ And
$$I(G)^T I(G)$$
I know how to find an incidence matrix of a graph and how to transpose a matrix . But how can we answer this question for all possible matrixes? Is it enough to pose an example and solve this question? Can we generalize the answer of a specific matrix for every single matrix ?
The book also mentioned that the answer is a particular kind of matrix because of the shape of it. I can really appreciate a hint on this.
What is Incedence matrix of a graph ? https://en.m.wikipedia.org/wiki/Incidence_matrix