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If A ,B ,A+I ,A+B are idempotent matrice...

If `A ,B ,A+I ,A+B` are idempotent matrices, then `A B` is equal to

A

`BA`

B

`-BA`

C

`I`

D

`O`

Text Solution

Verified by Experts

The correct Answer is:
B
Given `A, B, A + I, A+B` are idempotent. Hence,
`A^(2)=A, B^(2)=B, (A+I)^(2)=A+I` and `(A+B)^(2)=A+B`
`implies A^(2)+B^(2)+AB+BA=A+B`
`implies A+B+AB+BA=A+B`
`implies AB+BA=O`
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