Q69 / 125 · BITSAT 2011 · Mathematics

If \(A=\left[\begin{array}{lll}2 & 0 & 0 \\ 2 & 2 & 0 \\ 2 & 2 & 2\end{array}\right]\), then \(\operatorname{adj}(\operatorname{adj} A)\) is equal to -

  • A
    \(8\left[\begin{array}{lll}1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1\end{array}\right]\)
  • Correct answer
    B
    \(16\left[\begin{array}{lll}1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1\end{array}\right]\)
  • C
    \(64\left[\begin{array}{lll}1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1\end{array}\right]\)
  • D
    None of these

Solution

\(|A|=\left[\begin{array}{lll} 2 & 0 & 0 \\ 2 & 2 & 0 \\ 2 & 2 & 2 \end{array}\right]=(2)(2)(2)=8\) Now adj \((\operatorname{adj} A)=|\mathrm{A}|^{3-2} \mathrm{~A}\) \(=8\left[\begin{array}{lll} 2 & 0 & 0 \\ 2 & 2 & 0 \\ 2 & 2 & 2 \end{array}\right]=16\left[\begin{array}{ccc} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1 \end{array}\right]\)

Hence, the correct answer is option: 'B'.

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