  Wishart matrices are one of the fundamental matrix models in multivariate
statistics. We consider the classical $(m,n,\beta)$-Laguerre ensemble and give
a necessary and sufficient condition for finite moments for the inverse of
$(m,n,\beta)$-Laguerre matrices to exist. We extend the result to inverse
compound Wishart matrices for the values of $\beta = 1$ and $2$. Our result
complements the result by Letac and Massam [6], Matsumoto [7] and Collins et
al. [1].
