find the given expression

Question

1.  
    
2.  
3.  
4.  

Answer 1

Q = PAP^T

= P^T(Q²⁰¹⁶)P

= P^T * PAP^T * PAP^T * PAP^T * .......... * PAP^T​​​​​​​ * P

now |P^T * P| = 1

so all P^T ​​​​​​​* P will become 1

ultimately we will get final value as A²⁰¹⁶

now,

Value of |A| = 1*1 - 0*1 = 1

so |A²⁰¹⁶| = 1²⁰¹⁶ = 1

Only first option is matching, so answer should be option 1

You can also solve by finding A² then A³ and obtain the pattern to get A²⁰¹⁶

Comments

thanks a lot

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How  |PT * P|= 1?

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I also did not understand how P Transpose * P = 1 ??..If it was inverse we can prove like this...or maybe I am not understanding something here..

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Yeah i was wrong there. After watching my answer again. I also dont understand what i did there.