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If `A=[1 2 2 2 1-2a2b]` is a matrix satisfying the equation `AA^T=""9I` , where `I` is `3xx3` identity matrix, then the ordered pair (a, b) is equal to : (1) `(2,-1)` (2) `(-2,""1)` (3) (2, 1) (4) `(-2,-1)`
A. (2, -1)
B. (-2, 1)
C. (2, 1)
D. (-2, -1)

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Correct Answer - D
`A A^(T)=9I`
`implies [(1,2,2),(2,1,-2),(a,2,b)][(1,2,a),(2,1,2),(2,-2,b)]=9[(1,0,0),(0,1,0),(0,0,1)]`
`implies [(9,0,a+4+2b),(0,9,2a+2-2b),(a+4+2b,2a+2-2b,a^(2)+4+b^(2))]=[(9,0,0),(0,9,0),(0,0,9)]`
`implies a+4+2b=0, 2a+2-2b=0, a^(2)+4+b^(2)=9`
`implies a=-2, b=-1`

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