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Question

A square matrix satisfying Ak+1=A is called as periodic matrix.

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


A

True

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B

False

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Solution

The correct option is B

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.


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