Source of theorem regarding triangle presence in the graph

Question

I know that there exists a theorem that states the following. Graph $G$ contains a triangle if and only if there exist indices $i$ and $j$ so the both matrices $A_G$ and $A_G^2$ will have nonzero ($i,j$). However, I don't know the source of this theorem and I was unable to find it. Can you please give me a hint on where should I look for?

Answer 1

It's not really a "theorem": if $A_G$ (resp. $A^2_G$) have a non-zero values at $(i,j)$ it simply means there's a path of length 1 (resp. 2) between $i$ and $j$. Hence a triangle. The equivalence should write itself