# Can you give me some concrete examples of magmas?

I’ve seen the following (e.g. here):

I’ve learned a bit about groups and I could give examples of groups, but when reading the given table, I couldn’t imagine of what a magma would be. It has no associativity, no identity, no divisibility and no commutativity. I can’t imagine what such a thing would be. Can you give a concrete example of a magma?

A (“strict”) magma you’ve probably heard of is the vector cross-product in $$R3\Bbb R^3$$:
$$(a,b,c)×(x,y,z)=(bz−cy,cx−az,ay−bx) (a, b, c)\times(x, y, z) = (bz - cy, cx - az, ay - bx)$$
$$R3\Bbb R^3$$ is closed under this operation, but it has neither associativity, commutativity, identity nor divisibility.