b
(b) ${a_{ij}} = \frac{1}{2}(3i - 2j)$
==> ${a_{11}} = 1/2,\,\,\,{a_{12}} = - 1/2$ and ${a_{21}} = 2,\,\,\,{a_{22}} = 1$
$\therefore $ $A = {[{a_{ij}}]_{2 \times 2}} = \left[ {\begin{array}{*{20}{c}}{{a_{{\rm{11}}}}}&{{a_{12}}}\\{{a_{{\rm{21}}}}}&{{a_{22}}}\end{array}} \right]$
$\therefore $ $A = \left[ {\begin{array}{*{20}{c}}{1/2}&{ - 1/2}\\2&1\end{array}} \right]$.