Let M ∈ Mat n ( Q ) {\displaystyle {}M\in \operatorname {Mat} _{n}(\mathbb {Q} )} . Show that it does not make a difference, whether we compute the determinant in Q {\displaystyle {}\mathbb {Q} } , in R {\displaystyle {}\mathbb {R} } , or in C {\displaystyle {}\mathbb {C} } .