2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69482Let $A$ and $B$ be unital Banach algebras with $A$ a subalgebra of $B$. Denote the algebra of all $n\times n$ matrices with entries from $A$ by $M_{n}(A)$. In this paper we prove some results concerning the open question: If $A$ is inverse closed in $B$, then is $M_{n}(A)$ inverse closed in $M_{n}(B)$? We also study related questions in the setting where $A$ is a symmetric Banach *-algebra.6 pages, no figures, no tablesFunctional Analysistext