## Operations on positive definite matrices

Show that for positive definite matrices $$\mathbf A$$ and $$\mathbf B$$:
The matrix $$\mathbf A+\mathbf B$$ is also positive definite.
The matrix $$\mathbf A^{-1}$$ is also positive definite (i.e. show also that $$\mathbf A$$ is regular).