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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 [tex]\LARGE RE_{11}+...+RE_{n-1,n-1}[/tex] (where [tex]\LARGE E_{ij}[/tex] is n*n matrix whose ij th element is 1 and the others are 0)

what is the proof of the above statements .

Thanks