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Question: Answered & Verified by Expert
If $A=\left[\begin{array}{cc}2 & -3 \\ 4 & 1\end{array}\right]$, then $A+\operatorname{adj} A$ is
MathematicsMatricesMHT CETMHT CET 2022 (10 Aug Shift 2)
Options:
  • 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:
2684 Upvotes Verified Answer
The correct answer is: $\left[\begin{array}{ll}3 & 0 \\ 0 & 3\end{array}\right]$
$A+\operatorname{adj}(A)=\left[\begin{array}{cc}2 & -3 \\ 4 & 1\end{array}\right]+\left[\begin{array}{cc}1 & 3 \\ -4 & 2\end{array}\right]=\left[\begin{array}{ll}3 & 0 \\ 0 & 3\end{array}\right]$

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