In 1979, Pang proved that within the class of semimonotone matrices, R-matrices are Q-matrices and conjectured that the converse is also true. Jeter and Pye gave a counterexample when n= 5 for the converse; namely, they gave a semimonotone matrix that is in Q but not in R. In this paper, we prove this conjecture for semimonotone matrices of order n≤ 3 and provide a counterexample when n> 3 , showing the sharpness of the result. We also provide an application of this result.