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Consider the element in SL(2, R). What is the order of A

Chapter 3, Problem 53E

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QUESTION:

Consider the element \(A=\left[\begin{array}{ll}1 & 1 \\0 & 1\end{array}\right]\) in SL(2, R). What is the order of A? If we view \(A=\left[\begin{array}{ll}1 & 1 \\0 & 1\end{array}\right]\) as a member of \(S L\left(2, Z_{p}\right)\) (p is a prime), what is the order of A?

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QUESTION:

Consider the element \(A=\left[\begin{array}{ll}1 & 1 \\0 & 1\end{array}\right]\) in SL(2, R). What is the order of A? If we view \(A=\left[\begin{array}{ll}1 & 1 \\0 & 1\end{array}\right]\) as a member of \(S L\left(2, Z_{p}\right)\) (p is a prime), what is the order of A?

ANSWER:

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Given A =  

 

In general,

 

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