## matrix a^2

Such a matrix is called idempotent.

**Idempotent matrix**

In linear algebra, an idempotent matrix is a matrix which, when multiplied by itself, yields itself.That is, the matrix A is idempotent if and only if A2 = A

### matrix a^2 = a

**Examples of 2 × 2 idempotent matrices**

\begin{bmatrix}1 \ 1\\2 \ 3\end{bmatrix}\begin{bmatrix}3 \ 5 \\8 \ 1\end{bmatrix}