If A is idempotent and A + B = I, then which of the followin... | MATH - TYPES OF MATRICES, ALGEBRA OF MATRICES | SolveeIt | Solveeit

Today, August 19

Question

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

A

B is idempotent

B

AB = 0

C

BA = 0

D

All of these

Answer

All of these

Explanation

Solution

A + B = I ̃ B = I – A

Now B² = (I – A) (I – A) = I² – AI – IA + A²

= I – A – A + A

= I – A = B

\ B is idempotent

Now , AB = A (I – A) = AI – A² = A – A = a

Mse , BA = (I – A) = IA – A² = A – A = 0

Hence all are true