is it true that $\det(I+A)=?iso-8859-1?Q?=3E0$_=2C_if_$\det?=(A)=?iso-8859-1?Q?=3E0$=3F_=96_math.stackexchange.com?=

is it true that $\det(I+A)>0$ , if $\det(A)>0$? – math.stackexchange.com

I saw an inequality for $n\times n$ matrices. I was wondering if the
inequality is true or not? Does $\det(A)>0$ imply $\det(I+A)>0$?