Is it true that the generator of maximal ideal in $M_n(P[x])$ can be choosen to be monic?

Question

Let $P$ be a finite field and $R=M_n(P[x])$ be a matrix polynomial ring. I want to prove that for every polynomial (not necessary with invertible leading term) $A(x)\in R$ such that $R\cdot A(x)$ is a maximal left ideal there exists a unique monic polynomial $B(x)\in R$ such that $$ R\cdot A(x) = R\cdot B(x) $$

Crossposted ME.