How to prove convexity of that function of a symmetric matrix?

Question

Let $f(\Phi) = \|\Phi^{-1/2}a\|^{-2}_2=\left( a^T \Phi^{-1} a \right)^{-1}$ where
$\Phi \in \mathbb{R}^{n \times n}$ is a positive semi-definite normal matrix, e.g. a covariance matrix
$a \in \mathbb{R}^n$ is a vector

How to prove that $f$ is concave (that is, -$f$ is convex)?