In this paper, we have characterizations of idempotent matrices over general Boolean algebras and chain semirings. As a consequence, we obtain that a fuzzy matrix A = [a_i,j_] is idempotent if and only if all a_i,j_-patterns of A are idempotent matrices over the binary Boolean algebra B₁ = {0, 1} Furthermore, it turns out that a binary Boolean matrix is idempotent if and only if it can be represented as a sum of line parts and rectangle parts of the matrix.
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