##### Exercise7

Determine whether the following statements are true or false and provide a justification for your response.

1. The eigenvalues of a diagonal matrix are equal to the entries on the diagonal.

2. If $$A\vvec=\lambda\vvec\text{,}$$ then $$A^2\vvec=\lambda\vvec$$ as well.

3. Every vector is an eigenvector of the identity matrix.

4. If $$\lambda=0$$ is an eigenvalue of $$A\text{,}$$ then $$A$$ is invertible.

5. For every $$n\times n$$ matrix $$A\text{,}$$ it is possible to find a basis of $$\real^n$$ consisting of eigenvectors of $$A\text{.}$$

in-context