This site is supported by donations to The OEIS Foundation.

# Nonunits

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. ${\displaystyle \scriptstyle 0\,\cdot \,k\,=\,0,\,\forall k,\,}$ it cannot have a multiplicative inverse).

## Nonunits in the set of integers

The nonunits in the set ${\displaystyle \scriptstyle \mathbb {Z} \,}$ 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.)