LetR = Mn(F) the ring consists of all n*n matrices over a finite field F and
E= E11 + E22 + ... + En-1,n-1, where Eii is the elementary matrix(Eij is matrix whose ij th element is 1 and the others are 0). Then the following hold:
1. RE is a maximal left ideal.
2. If A is a rank n-1 matrix in R then A is similar to E.
what is the proof of the above statements?