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  • A square matrix P satisfies   where I is identity matrix. If<img alt="P^{n}=13I-21P,"

A square matrix P satisfies P^{2}=I-P  where I is identity matrix. IfP^{n}=13I-21P,then n is

 

Option: 1

6


Option: 2

8


Option: 3

9


Option: 4

10


Answers (1)

best_answer

Answer (2)

\\ \because P2 = I -P\\\Rightarrow P^{3} = 2P - I\\ \: \: \:
    \\ P^{4} = 2I -3P\\ P^{5} = 5P -3I \\ P^{6} = 5I -8P\\ P^{7} = 13P -8I\\P^{8} = 13I =21P

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Kuldeep Maurya

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