Is Every Rank n-1 Matrix in Mn(F) Similar to a Specific Elementary Matrix?

[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

 

[radou]

You need to prove that any matrix of rank n-1 can be transformed to a similar elementary matrix of rank n-1 by applying a finite number of elementary row/column transformations.

 

[xixi]

You need to prove that any matrix of rank n-1 can be transformed to a similar elementary matrix of rank n-1 by applying a finite number of elementary row/column transformations.

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}
how can I say that?