- Each field of characteristic zero contains a copy of the rational number field.
- For an $n$ by $n$ matrix $A,$ if it is not invertible, then there exists an $n$ by $n$ matrix $B$ such that $AB=0$ but $B\ne0.$
For (1), I think I have to use the fact that each subfield of the complex number field contains every rational number. Am I right? For (2), I have no idea what to do first.