If $A \succ B$, then $\operatorname{per} A \ge \operatorname{per} B$

Question

Let the matrices $A, B, A-B$ be positive definite. How to show $\operatorname{per} A \ge \operatorname{per} B$, where $\operatorname{per}$ denotes the permanent function?

Also, if $A$ is a $n\times n$ doubly stochastic matrix that is also positive semidefinite. Let $J$ be the matrix with all entries $1/n$. How to show $A-J$ is also positive semidefinite?