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!