Chapter 7.CR, Problem 64CR

(a) Find a symmetric matrix B such that $B^2=A$ for

$A=\left[\begin{array}{cc}2& 1\\ 1& 2\end{array}\right]$

(b) Generalize the result of part (a) by proving that if A is an $n\times n$ symmetric matrix with positive eigenvalues, then there exists a symmetric matrix B such that $B^2=A$.