# Inverses of leading principal minors are leading principal minors of inverse

What can one say about a matrix for which the inverse of each leading principal minor is equal to the leading principal minor of its inverse (of the same dimensions, of course)? For example, will this matrix necessarily be diagonal?

-
$\left[ {{1\ a}\atop {0\ 1}} \right]$ –  Allen Knutson Apr 10 at 20:47