Explanation

(b)
For the reaction,
$SO_{2}(g) + \frac{1}{2}O_{2}(g) \rightleftharpoons SO_{3}(g)$
Equilibrium constant, $K_{1} = \frac{\lbrack SO_{3}\rbrack}{\left\lbrack SO_{2} \right\rbrack\left\lbrack O_{2} \right\rbrack^{\frac{1}{2}}}$ …(i)
For the reaction,
$2{SO}_{3}(g) \rightleftharpoons 2{SO}_{2}(g) + O_{2}(g)\$
Equilibrium constant, $K_{2} = \frac{\left\lbrack SO_{2} \right\rbrack^{2}\lbrack O_{2}\rbrack}{\left\lbrack SO_{3} \right\rbrack^{2}}$ …(ii)
On squaring both sides in Eq.(i), we get
$K_{1}^{2} = \frac{\left\lbrack SO_{3} \right\rbrack^{2}}{\left\lbrack SO_{2} \right\rbrack^{2}\lbrack O_{2}\rbrack}$ …(iii)
Eq. (ii) $\times$ Eq (iii), we get
$K_{1}^{2} \times K_{2} = 1$
or $K_{2} = \frac{1}{K_{1}^{2}}$
or $K_{1}^{2} = \frac{1}{K_{2}}$