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 , 6 Years ago
Grade 12th pass
Magical Mathematics[Interesting Approach]> Let A be a square matrix and A^2=I, then ...
1 AnswersYash Chourasiya
Last Activity: 4 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−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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