Let A be a n × n matrix such that | A |=2. If the determinant of the matrix Adj (2 · Adj (2 A^-1)) · is 2^84, then n is equal to ____.

Let A be a $\displaystyle n \times n$ matrix such that $\displaystyle |\mathrm{A}|=2$. If the determinant of the matrix $\displaystyle \operatorname{Adj}\left(2 \cdot \operatorname{Adj}\left(2 \mathrm{~A}^{-1}\right)\right) \cdot$ is $\displaystyle 2^{84}$, then n is equal to $\displaystyle \_\_\_\_$.