QJEEM22Mae3fe: JEE Main 2022 Mathematics - Class 12 JEEM22Mae3fe Solution: Let A = ( 1 + i 1 − i 0 ) where . Then, the number of elements…

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QJEEM22Mae3fe: JEE Main 2022 Mathematics - Class 12 JEEM22Mae3fe Solution: Let A = ( 1 + i 1 − i 0 ) where . Then, the number of elements…

Let $A = (\begin{matrix} 1 + i & 1 \\ - i & 0 \end{matrix})$ where $i = \sqrt { - 1}$ . Then, the number of elements in the set { n $\in$ {1, 2, ......, 100} : Aⁿ = A } is ____________.

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$\therefore$ $A^{2} = [\begin{matrix} 1 + i & 1 \\ - i & 0 \end{matrix}] [\begin{matrix} 1 + i & 1 \\ - 1 & 0 \end{matrix}] = [\begin{matrix} i & 1 + i \\ 1 - i & - i \end{matrix}]$

$A^{4} = [\begin{matrix} i & 1 + i \\ 1 - i & - i \end{matrix}] [\begin{matrix} i & 1 + i \\ 1 - i & - i \end{matrix}] = I$

So A⁵ = A, A⁹ = A and so on.

Clearly n = 1, 5, 9, ......, 97

Number of values of n = 25

QJEEM22Mae3fe: JEE Main 2022 Mathematics - Class 12 JEEM22Mae3fe Solution: Let A = ( 1 + i 1 − i 0 ) where . Then, the number of elements…

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