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Nonunits are elements of a set (e.g. of numbers, matrices, polynomials, ...) without a multiplicative inverse in the given set. Zero is a nonunit in any set (since 0 is the multiplicative absorption element, i.e. it cannot have a multiplicative inverse).

Nonunits in the set of integers

The nonunits in the set of integers are

while the units are

  • {–1, +1}

Nonunits in the set of matrices

Nonunit matrices have determinant equal to zero. (Matrices with nonzero determinant are invertible.)