Periodic Matrix

Q.

A square matrix satisfying $A^{k+1}=A$ is called as periodic matrix.

If k = 2 satisfies the above condition, A becomes an idempotent matrix

1. True

2. False

Q.

A square matrix A such that $A^k=A$ for a positive integer k is called a periodic matrix.

1. True

2. False

Q.

A= $\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$which of the following is true?

1. A is a periodic matrix with period 1

2. A is an idempotent matrix

3. A is a periodic matrix with period 2

4. A is not an idempotent matrix