  We show that the maximal number of equal entries in a totally positive (resp.
totally nonsingular) $n\textrm{-by-}n$ matrix is $\Theta(n^{4/3})$ (resp.
$\Theta(n^{3/2}$)). Relationships with point-line incidences in the plane,
Bruhat order of permutations, and $TP$ completability are also presented. We
also examine the number and positionings of equal $2\textrm{-by-}2$ minors in a
$2\textrm{-by-}n$ $TP$ matrix, and give a relationship between the location of
equal $2\textrm{-by-}2$ minors and outerplanar graphs.
