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# Nonunits

From OeisWiki

**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

- Zero
- Prime numbers (positive primes and their negative associates)
- Composite numbers (positive composites and their negative associates)

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.)