QJEEM21Maab99: JEE Main 2021 Mathematics - Class 11 JEEM21Maab99 Solution: Let S = { n ∈ N

Let $$X=\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)$$ & $$A={\left(\begin{array}{cc}0& i\\ 1& 0\end{array}\right)}^n$$

$\Rightarrow$ AX = IX

$\Rightarrow$ A = I

$$\Rightarrow {\left(\begin{array}{cc}0& i\\ 1& 0\end{array}\right)}^n=I$$

$$\Rightarrow A^8=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$$

$\Rightarrow$ n is multiple of 8

So, number of 2 digit numbers in the set

S = 11 (16, 24, 32, .........., 96)