# Inverse Fisher Information Matrix multivariate normal distribution

Let $$X \sim N(0, \Sigma)$$ be a bivariate normal distribution with $$\Sigma \in \mathbb{R}^{2 \times 2}$$ and know mean of $$(0,0)^\intercal$$. I know how to calculate Fisher information matrix of $$X$$, but I would like to know if the inverse of the Fisher information matrix exists in this case.

I need this to show that, for a certain theorem, the regularity conditions are met.