I have an $N \times N$ orthogonal projection matrix $P = A^H(AA^H)^{-1}A$ that I'm trying to find the inverse for. I'm using matlab, however, I keep getting the warning "the matrix is close to singular or badly scaled". Now I'm wondering if it's even invertible. 

Are orthogonal projection matrices invertible and if so, is there any stable method for computing the inverse?