The Moore-Penrose pseudoinverse $A^+$ of a tall matrix $A \in \mathbb{R}^{m \times n}$ (with $m > n$ and full rank) is given by $A^+ = (A^T A)^{-1}A^T$. For $A = \begin{pmatrix} 1 & 0 \\ 0 & 1 \\ 0 & 0 \end{pmatrix}$, compute $A^+$.