Divergence with uniformly elliptic coefficient

Question

Let $A=A(x)$ be a matrix uniformly elliptic with $L^\infty$ coefficient, i.e. there exist $0<\lambda<\Lambda<+\infty$ such that $$ \lambda |\xi|^2 \leq (A\xi, \xi)\leq \Lambda |\xi|^2 $$ for all $\xi \in \mathbb{R}^n$. Then, given $X=(x_1,\cdots,x_n)$ is it true that $$ n\Lambda \leq \mbox{div}(AX)? $$ I'm aware that, if $A=Id$ and hence $\lambda=\Lambda =1$ the equality holds true, but I'm not even able to prove if the divergence of $AX$ is bounded from below and from above by some universal constants $C_1=C_1(n,\lambda,\Lambda), C_2=C_2(n,\lambda,\Lambda)$