1. Let A be a symmetric matrix with eigenvalues $\lambda_1, \dots, \lambda_n$. It is known that there exists an orthogonal matrix C such that $A = CDC^\prime$, where $D = diag(\lambda_1, \dots, \lambda_n)$. Use this fact to prove the following:
(a) $|A| = \lambda_1 \lambda_2 \dots \lambda_n$, where $|A|$ is the determinant of A.
(b) $trace\{A\} = \lambda_1 + \lambda_2 + \dots + \lambda_n$.