We investigate some equivalent conditions for the reverse order laws (ab)# = b
# and (ab)# = b
† in rings with involution. Similar results for (ab)# = b
a* and (ab)# = b*a
# are presented too.
Ben-Israel, A. and Greville, T. N. E., Generalized Inverses: Theory and Applications, 2nd ed., Springer, New York, 2003.
Cao, C., Zhang, X. and Tang, X., Reverse order law of group inverses of products of two matrices, Appl. Math. Comput., 158 (2004), 489–495.
Deng, C. Y., Reverse order law for the group inverses, J. Math. Anal. Appl., 382(2) (2011), 663–671.
Djordjević, D. S., Unified approach to the reverse order rule for generalized inverses, Acta Sci. Math. (Szeged), 67 (2001), 761–776.
Greville, T. N. E., Note on the generalized inverse of a matrix product, SIAM Rev., 8 (1966), 518–521.
Izumino, S., The product of operators with closed range and an extension of the reverse order law, Tohoku Math. J., 34 (1982), 43–52.
Hartwig, R. E. and Shoaf, J., Group inverses and Drazin inverses of bidiagonal and triangular Toeplitz matrices, J. Austral. Math. Soc., 24(A) (1977), 10–34.
Koliha, J. J. and Patrício, P., Elements of rings with equal spectral idempotents, J. Australian Math. Soc. 72 (2002), 137–152.
Penrose, R., A generalized inverse for matrices, Proc. Cambridge Philos. Soc., 51 (1955), 406–413.
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