I have a matrix C = {[1,1],[0,1],[1,0]}. And C^T (Transpose) = {[1,0,1], [1,1,0]}

When I multiply C*C^T, I get {[2,1,1],[1,1,0],[1,0,1]}

The question: What is the interpretation of the diagonal entries of C*C^T? My guess is they are the eigenvalues

When I multiply C^T*C, I get {[2,1],[1,2]}

Question: What do the entries of C^T*C represent? My guess is they are the eigenvectors

There is no book for this class, so I need help, please!