Abstract
Let R be an associative ring with identity 1. We describe all idempotent matrices with only zeros and ones on the diagonal in – the ring of upper triangular matrices over R (), and – the ring of infinite upper triangular matrices (indexed by ) over R. Moreover, when R is finite, we calculate the number of all idempotent matrices with only zeros and ones on the diagonal in .
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Disclosure statement
No potential conflict of interest was reported by the author.