What’s the Square matrix A equal to if a = a^2 ?

Last Updated On Tuesday 22nd Mar 2022

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

	[1 12 3][3 58 1]\begin{bmatrix}1  \    1\\2  \   3\end{bmatrix}\begin{bmatrix}3  \    5 \\8  \    1\end{bmatrix}
  

a 2 a matrix

matrix squared equals itself