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The zero matrix is the additive identity in . That is, for all it satisfies
There is exactly one zero matrix of any given size m×n having entries in a given ring, so when the context is clear one often refers to the zero matrix. In general the zero element of a ring is unique and typically denoted as 0 without any subscript indicating the parent ring. Hence the examples above represent zero matrices over any ring.
A matrix where just a single element is one and the rest are zero may be called a single-entry matrix.