Do hermitian matrices commute when they occupy they same elements but have different values?

Question

Given hermitian matrices A and B, they have different values but share the same non zero elements, e.g. $A=\begin{pmatrix}1&0&3\\0&2&4\\3&4&7\end{pmatrix}$ and $B=\begin{pmatrix}5&0&9\\0&7&1\\9&1&3\end{pmatrix}$

I am not familiar with the correct terminolgy, but in these examples you can see that the matrix A and B have zeros in the same "elements", the other elements are all non zero but are different.

Answer 1

Since$$AB=\begin{pmatrix}32 & 3 & 18 \\ 36 & 18 & 14 \\ 78 & 35 & 52\end{pmatrix}\text{ and }BA=\begin{pmatrix}32 & 36 & 78 \\ 3 & 18 & 35 \\ 18 & 14 & 52\end{pmatrix},$$the answer is negative.