Maths-

General

Easy

Question

# If A is idempotent and A + B = I, then which of the following true?

- B is idempotent
- AB = 0
- BA = 0
- All of these

## The correct answer is: All of these

### A + B = I B = I – A

Now B^{2}= (I – A) (I – A) = I^{2} – AI – IA + A^{2}

= I – A – A + A

= I – A = B

B is idempotent

Now , AB = A (I – A) = AI – A^{2} = A – A =

Mse , BA = (I – A) = IA – A^{2} = A – A = 0

Hence all are true

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