If $A = \left[ {\begin{array}{*{20}{c}} 1&2&2\\ 2&1&{ - 2}\\ a&2&b \end{array}} \right]$ is a matrix satisfying the equation $A{A^T} = 9I,$ where $I$ is $3 \times 3$ identity matrix, then the ordered pair (a, b) is equal to

JEE MATHEMATICS MCQ: MATRICES

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Application +4 | -1

A = \left[ {\begin{array}{cccccccccccccccccccc} 1&2&2\\ 2&1&{ - 2}\\ a&2&b \end{array}} \right]

is a matrix satisfying the equation

A{A^T} = 9I,

where

I

3 \times 3

identity matrix, then the ordered pair (a, b) is equal to

View answer and explanation

Correct option: D

(-2, -1)

Option D (-2, -1) is correct because, after substituting the matrix A into the equation AA^T = 9I and solving the resulting system of equations, the ordered pair (a, b) is found to be (-2, -1).

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