Q33 / 90 · JEE Main 2012 (26 May Online) · Mathematics

If $A=\left[\begin{array}{ccc}1 & 0 & 0 \\ 2 & 1 & 0 \\ -3 & 2 & 1\end{array}\right]$ and $B=\left[\begin{array}{ccc}1 & 0 & 0 \\ -2 & 1 & 0 \\ 7 & -2 & 1\end{array}\right]$ then $A B$ equals

  • Correct answer
    A
    $I$
  • B
    $A$
  • C
    $B$
  • D
    0

Solution

$$ \begin{aligned} & A=\left[\begin{array}{ccc} 1 & 0 & 0 \\ 2 & 1 & 0 \\ -3 & 2 & 1 \end{array}\right], B=\left[\begin{array}{ccc} 1 & 0 & 0 \\ -2 & 1 & 0 \\ 7 & -2 & 1 \end{array}\right] \\ & A B=\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]=I \end{aligned} $$

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

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