There is a 3 part question that I have been working on.
The first 2 parts are show that for a finite dimensional vector space:
is invertible if and only if and are invertible.
if and only if
Theese two I have successfully proven. It is the last part I am having trouble with which is:
Give an example for each that shows that the statements are false for infinite dimensional vector spaces.
Any help would be appreciated, Thanks!