Hey, I'm really struggling today.

We just started doing eigenvectors, and I'm supposed to solve this following problem without using determinants.

Prove that the eigenvectors of the matrix

2 0

0 2

generate a 2-Dimensional space and give a basis for it. Also, state the eigenvalues. I just don't think this stuff is harder than some of the other stuff I've done, but I'm really pathetic right now.