Matrix Time

Algebra Level 4

Given \[P = \begin{bmatrix} \cfrac { \sqrt { 3 } }{ 2 } & \cfrac { 1 }{ 2 } \\ \cfrac { -1 }{ 2 } & \cfrac { \sqrt { 3 } }{ 2 } \end{bmatrix}\] \[A = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}\] \[Q =\quad PA{ P }^{ T }\]

Evaluate \[{ P }^{ T }{ Q }^{ 2005 }P\]

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