Hi, I need to prove this statement, but my teacher wants me to so without using $\displaystyle adj{A}$ and I kind of stuck because using Cramer's rule to prove that is almost like using the $\displaystyle adj{A}$.

"$\displaystyle A\in M_n(\mathbb{Q})$ therefore $\displaystyle A\in M_n(\mathbb{R})$

prove that:if$\displaystyle A$ is nonsingular in$\displaystyle M_n(\mathbb{R})$, $\displaystyle A$ is also nonsingular in $\displaystyle M_n(\mathbb{Q})$"