Find the matrix

Algebra Level 3

P=[cosπ4sinπ4sinπ4cosπ4]X=[1212]P= \begin{bmatrix} \cos\cfrac { \pi }{ 4 } & -\sin\cfrac { \pi }{ 4 } \\ \sin\cfrac { \pi }{ 4 } & \cos\cfrac { \pi }{ 4 } \end{bmatrix} \qquad \qquad X = \left[ \begin{matrix} \cfrac { 1 }{ \sqrt { 2 } } \\ \cfrac { 1 }{ \sqrt { 2 } } \end{matrix} \right]

For matrices PP and XX as defined above, find P3XP^3X.

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