Question

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

• A. True
• B. False

Answer 1

The correct option is B

False

We have discussed that idempotent matrix is a square matrix satisfying

$A^2=A$ i.e. $A^{1+1}=A.$

If we compare $A^{1+1}=A$ with $A^{k+1}=A$, we get $A^{1+1}=A^{k+1}$

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.