InterviewSolution
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InterviewSolution
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If `A=[a b0a]`is nth root of `I_2,`then choose the correct statements:If `n`is odd, `a=1,b=0`If `n`is odd, `a=-1,b=0`If `n`is even, `a=1,b=0`If `n`is even, `a=-1,b=0`a. i, ii, iii, iv b.ii, iii, ivc. i, ii, iii, iv d. i,iii, ivA. i, ii, iiiB. ii, iii, ivC. i, ii, iii, ivD. i, iii, iv |
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Answer» Correct Answer - D If A is nth root of `I_(2)`, then `A^(n)=I_(2)`. Now, `A^(2)=[(a,b),(0,a)][(a,b),(0,a)]=[(a^(2),2ab),(0,a^(2))]` `A^(3)=A^(2) A=[(a^(2),2ab),(0,a^(2))][(a,b),(0,a)]=[(a^(3),3a^(2)b),(0,a^(3))]` Thus, `A^(n)=[(n^(n),na^(n-1)b),(0,a^(n))]` Now, `A^(n)=I implies [(a^(n),na^(n-1)b),(0,a^(n))]=[(1,0),(0,1)]` `implies a^(n)=1, b=0` |
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