Transform Wishart distribution to Chi-square distribution

Question

This's actually what I'm trying to prove: $$ \frac {a^{'}\Sigma^{-1}a}{a^{'}W^{-1}a} \sim \chi^{2}_{n-p+1} $$ $a$ is any P-dimensional nonzero constant vector, and $W \sim W_{p}(n,\Sigma)$, $\Sigma$ is a covariance matrix of p*p dimension.The key is that this inverse matrix is not easy to handle Thank for you answer.