We show, step-by-step, that the set of all 2 x 2 matrices with real entries forms a ring under addition and multiplication.

# Tag: monoid

## A Ring of Mappings

We show that the set of all mapping of real numbers with the operations of sums and products forms a commutative ring with identity.

## Composition of Mappings on a Set

We show that the set of all mappings from a set to itself with composition as an operation is a monoid, but not a group.