Find the matrix

Algebra Level 2

Let \[P\quad=\quad\begin{bmatrix} cos\cfrac { \pi }{ 4 } & -sin\cfrac { \pi }{ 4 } \\ sin\cfrac { \pi }{ 4 } & cos\cfrac { \pi }{ 4 } \end{bmatrix}\] and \[X\quad =\quad \left[ \begin{matrix} \cfrac { 1 }{ \sqrt { 2 } } \\ \cfrac { 1 }{ \sqrt { 2 } } \end{matrix} \right] \] Then \[{ P }^{ 3 }X\] is equal to

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