Isomorphic diagonal matrix spaces

[Jennifer1990]

Homework Statement

Is The space P2 is isomorphic to the space of all 3 × 3 diagonal matrices.

Homework Equations

The Attempt at a Solution

I know that P2 is isomorphic to vectors with 3 components so i think this statement is true, is it?

 

[CompuChip]

I think its true.
An elegant way to prove it is to show that the space of vectors with n components is isomorphic to the space of n x n diagonal matrices.

Then take n = 3 and compose isomorphisms :)