On the rank of a cograph

The rank of a graph is defined to be the rank of its adjacency matrix. Royle [G.F. Royle, The rank of a cograph, Electron. J. Combin. 10 (2003) #N11] proved a somewhat surprising result that the rank of a cograph is equal to the number of distinct non-zero rows of its adjacency matrix. In this paper we answer a question posed by Royle (2003) by giving an elementary short proof for a more general setting of this rank property of cographs.