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

If `A ,B ,A+I ,A+B` are idempotent matrices, then `A B` is equal to
A. `BA`
B. `-BA`
C. `I`
D. `O`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

Salim Ahmed Kawsar

Correct Answer - 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`

5 views Answered 2023-02-05 15:29

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