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

If $A=\left[\begin{array}{cc}2 & -3 \\ 4 & 1\end{array}\right]$, then $A+\operatorname{adj} A$ is
  1. $\left[\begin{array}{ll}3 & 0 \\ 0 & 3\end{array}\right]$
  2. $\left[\begin{array}{cc}1 & 3 \\ -4 & 2\end{array}\right]$
  3. $\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
  4. $\left[\begin{array}{cc}1 & -3 \\ 4 & 2\end{array}\right]$

Solution

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

Asked in: MHT CET 2022 (10 Aug Shift 2)

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