Problem: A) Let be an orthonormal basis for V. For any prove that

B) use (A) to prove that if is an orthonormal basis for V with inner product then for any where is the standard product on

Thoughts:

I worked out (A) but I am almost certain I did it wrong, however, this is what I did:

And I haven't the slightest idea what (B) means, let alone how to prove it using A which I almost certainly did wrong.