Q96 / 150 · MHT CET 2022 (10 Aug Shift 2) · Mathematics

If $A=\left[\begin{array}{cc}2 & -3 \\ 4 & 1\end{array}\right]$, then $A+\operatorname{adj} A$ is

  • Correct answer
    A
    $\left[\begin{array}{ll}3 & 0 \\ 0 & 3\end{array}\right]$
  • B
    $\left[\begin{array}{cc}1 & 3 \\ -4 & 2\end{array}\right]$
  • C
    $\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
  • D
    $\left[\begin{array}{cc}1 & -3 \\ 4 & 2\end{array}\right]$

Solution

$A+\operatorname{adj}(A)=\left[\begin{array}{cc}2 & -3 \\ 4 & 1\end{array}\right]+\left[\begin{array}{cc}1 & 3 \\ -4 & 2\end{array}\right]=\left[\begin{array}{ll}3 & 0 \\ 0 & 3\end{array}\right]$

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

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