Hi all.

I am a beginner to real maths and am looking at a problem from a book by Loomis and Sternberg.

Let be the linear transformation from to such that .

I need to show that is an isomorphism if is a bijection by showing that:

(a) injective -> surjective;

(b) surjective -> injective.

I'm not really sure where to start, and I can't even see the link between the properties of the 2 mappings; any hints would be greatly appreciated.

Thanks