A square matrix 
such that the matrix power 
for 
a positive integer is called a periodic matrix. If 
is the least such integer, then the matrix is said to have
period 
.
If 
,
then 
and 
is called idempotent.
Periodic Matrix
See also
Matrix PowerExplore with Wolfram|Alpha
References
Ayres, F. Jr. Schaum's Outline of Theory and Problems of Matrices. New York: Schaum, p. 11, 1962.Referenced on Wolfram|Alpha
Periodic MatrixCite this as:
Weisstein, Eric W. "Periodic Matrix." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PeriodicMatrix.html