Athira, S.K.Kamaraj, K.Johnson, P.S.2026-02-042023Eurasian Mathematical Journal, 2023, 14, 3, pp. 8-2520779879https://doi.org/10.32523/2077-9879-2023-14-3-08-25https://idr.nitk.ac.in/handle/123456789/22098We present more than 60 results, including some range inclusion results to characterize the reverse order law for the Moore-Penrose inverse of closed range Hilbert space operators. We use the basic properties of the Moore-Penrose inverse to prove the results. Some examples are also provided to illustrate failure cases of the reverse order law in an infinite-dimensional setting. © (2023). All Rights Reserved.closed range operatorMoore-Penrose inversereverse order law