Matrices And Determinants

Let for \(A = \left[ {\matrix{ 1 & 2 & 3 \cr \alpha & 3 & 1 \cr 1 & 1 & 2 \cr } } \right],|A| = 2\). If \(\mathrm{|2\,adj\,(2\,adj\,(2A))| = {32^n}}\), then \(3n + \alpha\) is equal to