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}