let R be a matrix ring over a finite field $\displaystyle F_{q}$ , i.e. $\displaystyle R=M_{n}(F_{q})$. then

1.Every matrix of rank n-1 in any maximal left ideal generates the maximal left ideal.

2.moreover,the number of matrices in every maximal left ideal that can be a generator is the same as the number of the generator matrices in the maximal left ideal $\displaystyle RE_{11}+...+RE_{n-1,n-1}$.

what is the proof of the above statements .

Thanks