An idempotent matrix is a square matrix which when multiplied by itself, gives the resultant matrix as itself. In other words, a matrix P is called idempotent if P2 = P.
Idempotent matrix Examples
The examples of 2 x 2 idempotent matrices are
This second matrix is the identity matrix.
The examples of 3 x 3 idempotent matrices are
How do you know if a matrix is idempotent?
It is easy to check whether a matrix is idempotent or not. Simply, check that square of a matrix is the matrix itself or not i.e. P2 = P, where P is a matrix. If this condition is satisfied then the matrix is idempotent. If the condition is not satisfied then the matrix is not idempotent.