Let ${J_{n,m}} = \int\limits_0^{{1 \over 2}} {{{{x^n}} \over {{x^m} - 1}}dx} $, $\forall$ n > m and n, m $\in$ N. Consider a matrix $A = {[{a_{ij}}]_{3 \times 3}}$ where $${a_{ij}} = \left\{ {\matrix{ {{j_{6 + i,3}} - {j_{i + 3,3}},} & {i \le j} \cr {0,} & {i > j} \cr } } \right.$. Then $\left| {adj{A^{ - 1}}} \right|$$ is :