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Misc. 13 - If A is such that A2 = I then - Class 12 Matrices

Misc. 13 - Chapter 3 Class 12 Matrices - Part 2

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Misc 13 If A =[■8("α" &"β" @"γ" &−"α" )] is such that A2 = I then A. 1 + α2 + βγ = 0 B. 1 – α2 + βγ = 0 C. 1 – α2 – βγ = 0 D. 1 + α 2 – βγ = 0 A = [■8("α" &"β" @"γ" &−"α" )] Given that A2 = I A . A = I [■8("α" &"β" @"γ" &−"α" )] [■8("α" &"β" @"γ" &−"α" )]= [■8(1&0@0&1)] [■8(𝛼. 𝛼+𝛽. 𝛾&𝛼. 𝛽+𝛽(−𝛼)@𝛾. 𝛼−𝛼. 𝛾&𝛾. 𝛽+(−𝛼)(−𝛼))]= [■8(1&0@0&1)] [■8(𝛼2+𝛽 𝛾&𝛼𝛽−𝛼𝛽@𝛼𝛾−𝛼𝛾&𝛾𝛽+𝛼2)]= [■8(1&0@0&1)] [■8(𝛼2+𝛽𝛾&0@0&𝛽𝛾+𝛼2)]= [■8(1&0@0&1)] Since the matrices are equal, corresponding element are equal ∴ 𝛼2+𝛽𝛾 = 1 0 = 1 – 𝛼2−𝛽𝛾 1 – 𝜶𝟐−𝜷𝜸 = 0 Hence, C is the correct answer

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.