Idempotent Element/Examples/Unit Matrix

Example of Idempotent Element

Let $\mathbf I_n$ be the unit matrix of order $n$.

Then $\mathbf I_n$ is idempotent under the operation of (conventional) matrix multiplication.

Proof

From Unit Matrix is Identity for Matrix Multiplication, $\mathbf I_n$ forms an identity element for matrix multiplication.

The result follows from Identity Element is Idempotent.

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): idempotent
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): idempotent