Definition:Modulo Multiplication/Also denoted as

Modulo Multiplication: Also denoted as
Although the operation of multiplication modulo $m$ is denoted by the symbol $\times_m$, if there is no danger of confusion, the conventional multiplication symbols $\times, \cdot$ etc. are often used instead.

The notation for multiplication of two integers modulo $m$ is not usually $\eqclass a m \times_m \eqclass b m$.

What is more normally seen is $a b \pmod m$.