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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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Misc 9 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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.