A periodic matrix with period 1, so that 
.
Idempotent Matrix
See also
Idempotent, Nilpotent Matrix, Periodic MatrixExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Idempotent Matrix." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/IdempotentMatrix.html