LetR=Mn(F) the ring consists of alln*nmatrices over a finite fieldFand

E=E11 +E22 + ... +En-1,n-1, whereEiiis the elementary matrix(Eij is matrix whose ij th element is 1 and the others are 0). Then the following hold:

1.REis a maximal left ideal.

2. IfAis a rankn-1 matrix inRthenAis similar toE.

what is the proof of the above statements?

thank you