inverse of $2\times2$ block matrix

I want to compute the inverse of the $2\times2$ block matrix $$\left(\begin{array}{cc} A & P\\ P^T & 0\\ \end{array}\right),$$ with $A$ an $n\times{n}$ matrix and $P$ and $n\times{m}$ matrix.

I only come across formulas for $$\left(\begin{array}{cc} A & B\\ C & D\\ \end{array}\right)^{-1}$$ that involve $D^{-1}$. However, in my case $D=0$, such that $D$ has no inverse and I don't know how to continue.

One of the formulas here does not involve $D^{-1}$