# Sign of a determinant based on sign conditions

New user here. I want to sign a determinant, using known qualitative conditions on the components. any help appreciated. dummy example below. thanks.

mat = {{a, b}, {c, c^2}};
MatrixForm[%] ;
det = FullSimplify[Det[mat]] ;
Sign[det] | a > 0 & b > 0 & c < 0

• Something like FullSimplify[Sign[Det[{{a, b}, {c, c^2}}]], a > 0 && b > 0 && c < 0]? – J. M.'s ennui Mar 24 '20 at 16:14
• You could also try Simplify[det > 0] to see the conditions, which are a c^2 > b c. – Chris K Mar 24 '20 at 16:15