Derivative of inverse matrix

Question

Suppose $\Omega \left( \mathbf{\alpha }\right) $ is a $T\times T$ full rank matrix where $\mathbf{\alpha }$ is a $p\times 1$ vector, then what's the exact expression for $\frac{\partial \Omega ^{-1}\left( \mathbf{\alpha }% \right) }{\partial \mathbf{\alpha }^{\prime }}?$ If $\mathbf{\alpha }$ is a scalar, then $$ \frac{\partial \Omega ^{-1}\left( \alpha \right) }{\partial \alpha }=-\Omega ^{-1}\frac{\partial \Omega ^{-1}\left( \alpha \right) }{\partial \alpha }% \Omega ^{-1},$$ but any reference for the case of $\mathbf{\alpha }$ is a vector? Thanks!