2 fixed grammar

If it was were reducible, all $n\times n$ matrices over any field extension of $K$ would have reducible characteristic polynomials. But consider the companion matrix of an irreducible polynomial over some not algebraically closed field extension of $K$.

1

If it was reducible, all $n\times n$ matrices over any field extension of $K$ would have reducible characteristic polynomials. But consider the companion matrix of an irreducible polynomial over some not algebraically closed field extension of $K$.