What do you call the element aside from the identity element which when a binary operation is applied to itself the product would be the identity element? example,

```
e * e = e <-- identity element
a * a = e <-- what do you call element a?
```

I have been searching for the term most appropriate for it but it seems that it doesn't have one.

If you do know what it is called, please tell me and please give me a link where i can read more about it. Thanks in advance!

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isn't it idempotent if a * a = a? i think the identity element for any group is idempotent, but what do you call element a if a * a = the identity element.

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Ah yes, my bad.

Self inverse

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