The number of diagonal matrix $A$ of order  $n$ are possible for which the equation  $A^3=A$ satisfies

If $A=\left[\begin{array}{ll}a& b\\ 0& a\end{array}\right]$ is $n^{\mathrm{th}}$ root of $I_2,$ then choose the correct statements:

$\left(\mathrm{i}\right)$ if $n$ is odd, $a=1, b=0$
$\left(\mathrm{ii}\right)$ if $n$ is odd,$a=-1, b=0$
$\left(\mathrm{iii}\right)$ if $n$ is even, $a=1, b=0$
$\left(\mathrm{iv}\right)$ if $n$ is even, $a=-1, b=0$

If $\left[\begin{array}{cc}2& -1\\ 1& 0\\ -3& 4\end{array}\right]A=\left[\begin{array}{ccc}-1& -8& -10\\ 1& -2& -5\\ 9& 22& 15\end{array}\right]$, then sum of all the elements of matrix $A$ is