Homeomorphism calculation help

[rifat]

How can we show that the set {A in GL(n;R) | det(A)>0} is homeomorphic to the set {A in GL(n;R) | det(A)<0}?"

 

[Dick]

If you think of A as a matrix, how about just replacing the first row with the negative of itself? Isn't that an explicit homeomorphism?