Chapter 3.1, Problem 31P

Eigenvalues and Eigenvectors. In each of Problems $13$ through $32$, find the eigenvalues and eigenvectors of the given matrix.

$A=\left(\begin{array}{cc}\frac{5}{4}& \frac{3}{4}\\ \frac{3}{4}& \frac{5}{4}\end{array}\right)$