Eigenvalue of multiplication of two matrix vs the eigenvalue of squared matrix

Question

$A$ and $B$ are two stochastic non-negative matrices. $B$ has the same value as $A$ but some rows and columns are displaced.

I was wondering if there is a way to proof: $\mathrm{SLEM}(A \cdot B) < \mathrm{SLEM}(A \cdot A)$

$\mathrm{SLEM}$ is second largest eigenvalue