A copositive Q-matrix which is notR0

Jeter and Pye gave an example to show that Pang's conjecture, thatL1 ⋂Q ⊂R0, is false while Seetharama Gowda showed that the conjecture is true for symmetric matrices. It is known thatL1-symmetric matrices are copositive matrices. Jeter and Pye as well as Seetharama Gowda raised the following question: Is it trueC0 ⋂Q ⊂R0? In this note we present an example of a copositive Q-matrix which is notR0. The example is based on the following elementary proposition: LetA be a square matrix of ordern. SupposeR1 =R2 whereRi stands for theith row ofA. Further supposeA11 andA22 are Q-matrices whereAii stands for the principal submatrix omitting theith row andith column fromA. ThenA is a Q-matrix.