Let A be a 3X3 skew-symmetric matrix. Show that I + A is invertible

where I is the identity matrix

Skew matrix A is A transpose =-A
So I + A=
1 a b
-a 1 c
-b -c 1
det(I+a)=
1(1+c^2) -a(-a+cb) +b(ac+b)=
1 +c^2+a^2 +b^2
This is always positive
So since determinant is non-zero it has an inverse