# Find the matrix

Algebra Level 3

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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