  We prove the nonsingularity of a class of integer matrices V(n,d), namely
power-product matrix, for positive integers n and d. Some technical proofs are
mainly based on linear algebra and enumerative combinatorics, particularly the
generating function method and involution principle. We will show that the
matrix V(n,d) is nonsingular for all positive integers n and d, and often with
sparse structure. Special attention is given to the computation of the
determinant V(2,d) with positive integer d.
