$\Rightarrow \mathrm{AX}=\mathrm{IX}$
$\Rightarrow \mathrm{A}=\mathrm{I}$
$\Rightarrow\left(\begin{array}{ll}0 & \mathrm{i} \\ 1 & 0\end{array}\right)^{n}=\mathrm{I}$
$\Rightarrow \mathrm{A}^{8}=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
$\Rightarrow \mathrm{n}$ is multiple of $8$
So number of $2$ digit numbers in the set
$\mathrm{S}=11(16,24,32, \ldots \ldots, .96)$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$f(x) = \left\{ {\begin{array}{*{20}{l}}
{\frac{{k\cos x}}{{\pi - 2x}},}&{{\rm{ if }}\,x\, \ne \,\frac{\pi }{2}}\\
{3,}&{{\rm{ if }}\,x\, = \,\frac{\pi }{2}}
\end{array}} \right.$ at $x = \frac{\pi }{2}$
$(i)$ $f (x)$ is bounded on $a \le x \le b.$
$(ii)$ The equation $f (x) = 0$ has at least one solution in $a < x < b.$
$(iii)$ The maximum and minimum values of $f (x)$ on $a \le x \le b$ occur at points where $f ' (c) = 0$.
$(iv)$ There is at least one point $c$ with $a < c < b$ where $f ' (c) > 0$.
$(v)$ There is at least one point $d$ with $a < d < b$ where $f ' (c) < 0.$