a
(a) $A = \left[ {\begin{array}{*{20}{c}}0&1&0\\1&0&0\\0&0&1\end{array}} \right]$ $ \Rightarrow $ $|A| = - 1(1 + 0) = - 1$
$adj(A) = \,\left[ {\,\begin{array}{*{20}{c}}{{A_{11}}}&{{A_{21}}}&{{A_{31}}}\\{{A_{12}}}&{{A_{22}}}&{{A_{32}}}\\{{A_{13}}}&{{A_{23}}}&{{A_{33}}}\end{array}\,} \right]$
$\Rightarrow$ ${A_{11}} = 0,\,{A_{12}} = - 1,\,{A_{13}} = 0$
${A_{21}} = - 1,\,{A_{22}} = 0,\,{A_{23}} = 0$
${A_{31}} = 0$, ${A_{32}} = 0,{A_{33}} = - 1$
$\Rightarrow$ ${A^{ - 1}} = \frac{{adj\,(A)}}{{|A|}} = \left[ {\,\begin{array}{*{20}{c}}0&1&0\\1&0&0\\0&0&1\end{array}\,} \right] = A$.