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

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

a 2 a matrix

matrix squared equals itself