Can we say that $X \in \Bbb M_3 (\Bbb Z)$?

Question

Let $A,XAX^{-1} \in \Bbb M_3 (\Bbb Z)$ for some $X \in \Bbb M_3 (\Bbb R).$ Then can we say that $X \in \Bbb M_3 (\Bbb Z)$?

Please help me in this regard.

Thank you very much.

Answer 1

Hint: Consider if $A$ is the identity matrix.