Let A be a self-inverse matrix ($A=A^{-1}$) with integer values such that no two integers have the same absolut value. Let M be the maximum of the absolut values (maximum-norm) of A. Which M is the least possible for a given size of A ?
There are no 2x2 - matrices with the desired property.
For 3x3-matrices , my current record is
[[ 13 , 8 , -16 ][-9 , -5 , 12 ][ 6 , 4 , -7 ]]
with M = 16
For 4x4-matrices , my current record is
[[ 29,-26, -24 , 18 ][ 15 , -14 , -12 , 9] [-6 , 7 , 5 , -3] [-33 , 31 , 28 , -20 ]]
with M = 33