Q82 / 225 · JEE Main 2004 · Mathematics

Let $A=\left(\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right)(10) B=\left(\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3\end{array}\right)$. If $B$

  • A
    $-2$
  • Correct answer
    B
    5
  • C
    2
  • D
    $-1$

Solution

$A B=I \Rightarrow A(10 B)=10 \mathrm{I}$ $\Rightarrow\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right]\left[\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3\end{array}\right]=\left[\begin{array}{ccc}10 & 0 & 5-\alpha \\ 0 & 10 & \alpha-5 \\ 0 & 0 & 5+\alpha\end{array}\right]=10\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$ if $\alpha=5$.

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

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