I am trying to determine constraints for a,b,c that are real, such that the eigenvalues of my system matrix have all negative real part.

restart;
with(LinearAlgebra):
assume(a,'real');
assume(b,'real');
assume(c,'real');
A:=<c,0,0;0,-1,a;0,b,-1>
elist:=Eigenvalues(A):
map(lprint,elist):
c
-1+(b*a)^(1/2)
-1-(b*a)^(1/2)

If all eigenvalues real part must be less than 0, then clearly:

c < 0

ab < 1

However, when trying to verify these results with "is" and "coulditbe" Maple gives me blatantly false results:

additionally(c<0)
additionally(a*b<1)
is(Re(-1+sqrt(a*b))<0)
                             false

coulditbe(Re(-1+sqrt(a*b))>0)
                              true

The real part of -1+sqrt(a*b) can never be greater than 0 under the assumption that ab<1. So why is Maple giving me nonsense? Am I using the commands incorrectly?