Modulo Multiplication has Identity

Theorem
Multiplication modulo $m$ has an identity:


 * $\forall \eqclass x m \in \Z_m: \eqclass x m \times_m \eqclass 1 m = \eqclass x m = \eqclass 1 m \times_m \eqclass x m$

Proof
Follows directly from the definition of multiplication modulo $m$:

Thus $\eqclass 1 m$ is the identity for multiplication modulo $m$.