Let R = Mn(F) the ring consists of all n*n matrices over a finite field F and(adsbygoogle = window.adsbygoogle || []).push({});

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

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# Ring of matrix over a field

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