Idempotent Element/Examples
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Examples of Idempotent Elements
Zero is Idempotent for Addition
$0$ is idempotent under the operation of addition in the set of integers $\Z$, but no other element of $\Z$ is so.
One is Idempotent for Multiplication
$1$ is idempotent under the operation of multiplication in the set of real numbers $\R$.
Unit Matrix
Let $\mathbf I_n$ be the unit matrix of order $n$.
Then $\mathbf I_n$ is idempotent under the operation of (conventional) matrix multiplication.