cycle in a directed graph

Hi I saw the answer: 

?If the graph has n nodes and is represented by an adjacency matrix, you can square the matrix (log_2 n)+1 times. Then you can multiply the matrix element-wise by its transpose. ?

I?m a PhD student working on my research and I need to check for cycles in a directed graph to make sure it is a DAG. The answer given is extremely useful but I need the theorem statement, or a reference. Do you have a book where this is stated or a paper?

Thanks!

Daniela.