A square matrix satisfying Ak+1=A is called as periodic matrix.
If k = 2 satisfies the above condition, A becomes an idempotent matrix
False
We have discussed that idempotent matrix is a square matrix satisfying
A2=A i.e. A1+1=A.
If we compare A1+1=A with Ak+1=A, we get A1+1=Ak+1
So k+1 = 1+1 i.e. k=1.
So the matrix becomes idempotent matrix for k=1 and not for k=2.
Hence the statement is False.