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If A = [[1, 2, 2], [2, 1, -2], [a, 2, b]] is a matrix satisfying the equation AA^T = 9I, where I is 3 × 3 identity matrix, then the ordered pair (a, b) is equal to:

1. (2, 1)
2. (-2, -1)
3. (2, -1)
4. (-2, 1)

Correct answer: (-2, -1)

Solution

Row1.Row3=a+4+2b=0 and Row2.Row3=2a+2-2b=0 give b=a+1 and 3a+6=0, so a=-2, b=-1. Thus (a,b)=(-2,-1).

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