let R be a matrix ring over a finite field F_{q} , i.e. 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 RE_{11}+...+RE_{n-1,n-1}.

what is the proof of the above statements .
Thanks