$A^{10}$ by computing $PD^{10}P^{-1}$

$A^{-1}$ by computing $PD^{-1}P^{-1}$ where $D^{-1} = \text{diag}(1, 1/2, 1/3)$

$\sqrt{A}$ by computing $P\sqrt{D}P^{-1}$ where $\sqrt{D} = \text{diag}(1, \sqrt{2}, \sqrt{3})$

All of the above