If A is involutary matrix, then which of the following is/are correct? Options: A . &nbspI + A is idempotent B . &nbspI – A is idempotent C . &nbsp(I + A)(I – A) is singular D . &nbspI+A3 is idempotent

If A is involutary matrix, then which of the following is/are correct?

Question

If A is involutary matrix, then which of the following is/are correct?

Options:

A . I + A is idempotent

B . I – A is idempotent

C . (I + A)(I – A) is singular

D . I+A3 is idempotent

Answer: Option C
:
C

A^{2} = I

(I + A) (I - A) = I - A^{2} + I - I = O

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