A question from Golan's linear algebra:
Let $A\in M(n,\mathbb R)$ (which denotes the set of all $n\times n$ matrices, for some $n\geq 2$) be symmetric. Does there exist a symmetric matrix $B$ such that $B^2=A$?
It asks again whether it is possible to find such a matrix in case $A$ is symmetric and positive definite? How to do this? Any hints to approach them. I am totally clueless