Let A be a square matrix and A^2=I, then show that at least one of I-A and I+A is singular

Question

Yash Chourasiya · Answer

Hello Student Given, A 2 = I ⇒ I − A 2 = ( I − A ) ( I + A ) = 0 ⇒ ∣ I − A ∣ ∣ I + A ∣ = 0 ∴ ∣ I − A ∣ = 0 or ∣ I + A ∣ = 0 i.e atleast one of ( I − A ) and ( I + A ) is singular. I hope this will help you.

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Let A be a square matrix and A^2=I, then show that at least one of I-A and I+A is singular

Let A be a square matrix and A^2=I, then show that at least one of I-A and I+A is singular

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Let A be a square matrix and A^2=I, then show that at least one of I-A and I+A is singular

Let A be a square matrix and A^2=I, then show that at least one of I-A and I+A is singular

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Other Related Questions on Magical Mathematics[Interesting Approach]

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