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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

Grade:12th pass

1 Answers

Yash Chourasiya
askIITians Faculty 256 Points
2 years ago
Hello Student
 
 
Given, A2=I
IA
 
2=(IA)(I+A)=0
IAI+A=0
IA=0 or I+A=0
i.e atleast one of (IA) and (I+A) is singular.
 
 
I hope this will help you.

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