Q76 / 150 · MHT CET 2022 (07 Aug Shift 1) · Mathematics

If matrix $\mathrm{A}=\left[\begin{array}{ll}1 & 2 \\ 4 & 3\end{array}\right]$ is such that $\mathrm{AX}=\mathrm{I}$, where $\mathrm{I}$ is $2 \times 2$ unit matrix, then $X=$

  • A
    $\frac{1}{5}\left[\begin{array}{ll}-3 & -2 \\ -4 & -1\end{array}\right]$
  • Correct answer
    B
    $\frac{1}{5}\left[\begin{array}{cc}-3 & 2 \\ 4 & -1\end{array}\right]$
  • C
    $\frac{1}{5}\left[\begin{array}{ll}3 & 2 \\ 4 & 1\end{array}\right]$
  • D
    $\frac{1}{5}\left[\begin{array}{cc}3 & -2 \\ -4 & 1\end{array}\right]$

Solution

$\mathrm{AX}=\mathrm{I} \Rightarrow \mathrm{X}=\mathrm{A}^{-1}=\mathrm{A}^{-1}$ $\Rightarrow X=\left[\begin{array}{ll}1 & 2 \\ 4 & 3\end{array}\right]^{-1}=\frac{-1}{5}\left[\begin{array}{cc}3 & -2 \\ -4 & 1\end{array}\right]=\frac{1}{5}\left[\begin{array}{cc}-3 & 2 \\ 4 & -1\end{array}\right]$

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

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