Let's define "Divergence" $$ \text{Div}A(x)=\left(\sum_{j=1}^{d}\frac{\partial a_{ij}}{\partial x_{j}}\right)_{1\leq i\leq d}, $$ where $A$ is a $d$ by $d$ matrix and $x\in\mathbb{R}^{d}$. I use capital D, which distinguishes the original divergence.
Here's my question :
Let's $B(y) := PA(P^{-1}y)P^{T}$. If $\text{Div}A(x)=0,$ then $\text{Div}B(y)=0$ where $P\in\text{GL}_{d}(\mathbb{R})$.
My trial : $$\sum_{l}^{d}\sum_{i,j}^{d}p_{1i}\left(\sum_{k}^{d}\frac{\partial a_{ij}\left(x\right)}{\partial x_{k}}\tilde{p_{kl}}\right)p_{lj}$$ where $P^{-1}=\left(\tilde{p}_{ij}\right)$. (I'm not sure)