If P = $$\left[ {\matrix{ {{{\sqrt 3 } \over 2}} & {{1 \over 2}} \cr { - {1 \over 2}} & {{{\sqrt 3 } \over 2}} \cr } } \right],A = \left[ {\matrix{ 1 & 1 \cr 0 & 1 \cr } } \right]\,\,\,$$ Q = PAPT, then PT Q2015 P is :

Question

If P = $$\left[ {\matrix{ {{{\sqrt 3 } \over 2}} & {{1 \over 2}} \cr { - {1 \over 2}} & {{{\sqrt 3 } \over 2}} \cr } } \right],A = \left[ {\matrix{ 1 & 1 \cr 0 & 1 \cr } } \right]\,\,\,$$

Q = PAP^T, then P^T Q²⁰¹⁵ P is :

$$\left[ {\matrix{ 0 & {2015} \cr 0 & 0 \cr } } \right]$$

$$\left[ {\matrix{ {2015} & 1 \cr 0 & {2015} \cr } } \right]$$

$$\left[ {\matrix{ {2015} & 0 \cr 1 & {2015} \cr } } \right]$$

$$\left[ {\matrix{ 1 & {2015} \cr 0 & 1 \cr } } \right]$$

Solution

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