A ring $R$ is a strongly clean ring if every element in $R$ is the sum of an idempotent and a unit that commutate. We construct some classes of strongly clean rings which have stable range one. It is shown that such cleanness of $2 imes 2$ matrices over commutative local rings is completely determined in terms of solvability of quadratic equations.

The main aim of this article is to study an extension the Beta and Gamma matrix functions by using a two-parameter Mittag-Leffler function. In particular, we investigate certain properties these extended such as symmetric relation, integral representations, summation relations, generating relation functional relation.