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Let S m Z Am Am 3I A6 where A 2 and 1 1 and 0 Then nS i... | (Mathematics) | DivineJEE

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Mathematics

Exam

Mathematics

Let

S = \{ m \in \mathbb{Z} : A^m + A^m = 3I - A^{-6} \}

, where

A = \begin{bmatrix} 2 & -1 \\ 1 & 0 \end{bmatrix}

. Then

n(S)

is equal to ______.

Explanation

$=\mathrm{m}^2+1+\mathrm{m}+1=8 \\$

$=\mathrm{m}^2+\mathrm{m}-6=0 \Rightarrow \mathrm{~m}=-3,2 \\$

$\mathrm{n}(\mathrm{~s})=2$

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