Let  be a ring with identity and equipped with involution " ". If  is element of  and has the Moore Penrose inverse, then  and  also have the Moore Penrose inverse. This paper found thatMoore Penrose inverse of is the same with the group inverse of  Also the Moore Penrose inverse of  is the same with the group inverse of Then the results of this investigation are used to  discusse the characteristic of the Moore Penrose inverse of elements in  through the group inverse .
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