LetR = Mn(F)be the ring consists of all n*n matrices over a fieldFand

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

I know thatREis a maximal left ideal . LetQbe an invertible matrix . Can we say thatREQis a maximal left ideal ?