In this paper, we present some new explicit identities of matrix powers and their proofs. For instance, AC+D=AC +ADand(AB)T=ABTfor matrices A‚B C.

Let $R$ be a ring with unity. The undirected nilpotent graph of $R$, denoted by $Gamma_N(R)$, is a graph with vertex set ~$Z_N(R)^* = {0neq x in R | xy in N(R) for some y in R^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in N(R)$, or equivalently, $yx in N(R)$, where $N(R)$ denoted the nilpotent elements of $R$. Recently, it has been proved that if $R$ is a left A...

       The purpose of this review article is to characterize all of the parameters regarding the types, polymers used, and release kinetics of matrix tablets. Matrix system was the earliest oral extended release platform for medicinal use. Matrix tablets are most commonly used methods to modulate the release profile of drugs. They are much desirable and preferred for such therapy because they o...

let r be a ring and v be a matrix valuation on r. it is shown that, there exists a correspondence between matrix valuations on r and some special subsets ?(mvpr) of the set of all square matrices over r, analogous to the correspondence between invariant valuation rings and abelian valuation functions on a division ring. furthermore, based on malcolmson’s localization, an alternative proof for t...