b
(b) We have, $A(adj\,A) = \left[ {\begin{array}{*{20}{c}}{10}&0\\0&{10}\end{array}} \right]$
or $A(adj\,A) = 10\,\left[ {\begin{array}{*{20}{c}}1&0\\0&1\end{array}} \right] = 10I$ …..(i)
and ${A^{ - 1}} = \frac{1}{{|A|}}\,(adj\,A)$
$A(adj\,A) = |A|\,I$…..(ii)
$\therefore $ From equation $(i) $ and $(ii)$, we get $|A| = 10$.