Explanation

(d)
We know that the expression $ax^{2} + bx + c > 0$ for all $x$, if $a > 0$ and $b^{2} < 4ac$.
$\therefore\left( a^{2} - 1 \right)x^{2} + 2(a - 1)x + 2$ is positive for all $x$, if
$a^{2} - 1 > 0\ \ and\ \ 4(a - 1)^{2} - 8\left( a^{2} - 1 \right) < 0$
$\Rightarrow a^{2} - 1 > 0\ \ and - 4(a - 1)(a + 3) < 0$
$\Rightarrow a^{2} - 1 > 0\ \ and\ \ (a - 1)(a + 3) > 0$
$\Rightarrow a^{2} > 1\ \ and\ \ a < - 3\ or\ a > 1$
$\Rightarrow a < - 3\ \ or\ \ a > 1$