Matrices And Determinants

Let \(A = \{ {a_{ij}}\}\) be a 3 \(\times\) 3 matrix,

where \({a_{ij}} = \left\{ {\matrix{ {{{( - 1)}^{j - i}}} & {if} & {i < j,} \cr 2 & {if} & {i = j,} \cr {{{( - 1)}^{i + j}}} & {if} & {i > j} \cr } } \right.\)

then \(\det (3Adj(2{A^{ - 1}}))\) is equal to _____________.