If $\mathrm{A}=\left[\begin{array}{ccc}3& 1& 2\\ 2& -3& -1\\ 1& 2& 1\end{array}\right]$ find $\mathrm{A} (adj \mathrm{A})$ without calculating $adj \mathrm{A}$.

Find the inverse of the matrix $\mathrm{A}=\left[\begin{array}{cc}\mathrm{a}& \mathrm{b}\\ \mathrm{c}& \frac{1+\mathrm{bc}}{\mathrm{a}}\end{array}\right]$ and show that

$a{\mathrm{A}}^{-1}=(a^2+bc+1)\mathrm{I}-a\mathrm{A}$.