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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

Pawan joshi , 7 Years ago
Grade 12th pass
anser 1 Answers
Yash Chourasiya

Last Activity: 5 Years ago

Hello Student
 
 
Given, A2=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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