Let $\text{Mat}(n\times n,\mathbb{Z})$ denote the collection of integer $n\times n$ matrices. We say $M\in \text{Mat}(n\times n,\mathbb{Z})$ is a *power matrix* if there is an integer $k>1$ and a matrix $A\in \text{Mat}(n\times n,\mathbb{Z})$ such that $A^k = M$. Let $\text{Pow}(n\times n,\mathbb{Z})$ denote the set of $n\times n$ power matrices.

Is the set $\text{Pow}(n\times n,\mathbb{Z})$ computable for every positive integer $n$?