# Ring of matrix over a field

1. Jan 30, 2010

### xixi

Let R = 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. If A is a rank n-1 matrix in RE then A is similar to E.

what is the proof of the above statement?
thank you

2. Feb 4, 2010

for similarity between A and E there must be an invertible matrix P such that $$\textit{P}$$$$\textit{A}$$$$\textit{\textit{P}}^{-1}$$$$\textit{=E}$$