I am facing difficulties in calculating the Moore-Pensore pseudoinverse of a positive semidefinite matrix $A$, where $A$ is self-adjoint and $\langle A u, u \rangle \geq 0$ for all $u \in \mathcal{H}$, where $\mathcal{H}$ is a complex Hilbert space. 

For example,

$$A = \begin{bmatrix} 1&-1\\ -1&1\end{bmatrix}$$ 

is a positive semidefinite matrix. How to calculate the Moore-Penrose pseudoinverse of $A$?