Showing GL(n,R) positive determinant is homeomorphic to negative determinant

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rifat
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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}?"
 
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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?
 

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