Eigenvalues: Real & Equal in Size but Opposite Signs

[Natasha1]

In my textbook recently I stumbled across the following:

Give a general description of those matrices which have two real eigenvalues equal in 'size' but opposite in sign? Could anyone explain this again very simply :-)

 

[0rthodontist]

What's to explain? They want you to describe the matrices that have two real eigenvalues of equal magnitude and opposite sign, such as 4 and -4.