Multiplicative Magic Square from 9 Terms of Geometric Sequence from 1, 2, 4

Problem

With the first $9$ terms of the geometric sequence $1, 2, 4, \ldots$,

form a product of $4096$ each way.

$\begin{array}{|c|c|c|}

\hline 2 & 64 & 32 \\ \hline 256 & 16 & 1 \\ \hline 8 & 4 & 128 \\ \hline \end{array}$

$\begin{array}{|c|c|c|}

\hline 2 & 7 & 6 \\ \hline 9 & 5 & 1 \\ \hline 4 & 3 & 8 \\ \hline \end{array}$

Subtract $1$ from each element:

$\begin{array}{|c|c|c|}

\hline 1 & 6 & 5 \\ \hline 8 & 4 & 0 \\ \hline 3 & 2 & 7 \\ \hline \end{array}$

This square is still magic.

Now replace each element $n$ with $2^n$:

$\begin{array}{|c|c|c|}

\hline 2^1 & 2^6 & 2^5 \\ \hline 2^8 & 2^4 & 2^0 \\ \hline 2^3 & 2^2 & 2^7 \\ \hline \end{array}$

which is:

$\begin{array}{|c|c|c|}

\hline 2 & 64 & 32 \\ \hline 256 & 16 & 1 \\ \hline 8 & 4 & 128 \\ \hline \end{array}$

$\blacksquare$