Question

How do I find the eigenspace of the identity matrix. I know the eigenvalue is 1, but what now?

Answer 1

Eigenspace is the set of all eigenvectors of the identity matrix, right? But it only has one eigenvalue, so you're looking for all the vectors such that
\[\huge I\vec{v}=1\cdot\vec{v}\]

Answer 2

But isn't any vector multiplied by I the vector? So couldn't any vector work?

Answer 3

Yeah, my point exactly :)

Answer 4

So how is that represented as an eigenspace? Do I have a basis or?

Answer 5

I'd think the standard basis, with dimension equal to the dimension of the identity matrix you used...