If A= [ ll -1 & 5 -3 & 2 ], then adj A= - Vidyadip

MCQ

If $A=\left[\begin{array}{ll}-1 & 5 \\ -3 & 2\end{array}\right]$, then adj $A=$

A
$\left[\begin{array}{cc}2 & 3 \\ -5 & -1\end{array}\right]$
B
$\left[\begin{array}{ll}1 & -5 \\ 3 & -2\end{array}\right]$
✓
$\left[\begin{array}{ll}2 & -5 \\ 3 & -1\end{array}\right]$
D
$\left[\begin{array}{ll}-2 & 5 \\ -3 & 1\end{array}\right]$

✓

Answer

Correct option: C.

$\left[\begin{array}{ll}2 & -5 \\ 3 & -1\end{array}\right]$

(C) Matrix of co-factors $=\left[ A _{ ij }\right]_{2 \times 2}$
$=\left[\begin{array}{ll} A _{11} & A_{12} \\ A_{21} & A_{22}\end{array}\right]$
$=\left[\begin{array}{cc}2 & -(-3) \\ -5 & -1\end{array}\right]$
$=\left[\begin{array}{cc}2 & 3 \\ -5 & -1\end{array}\right]$
$\therefore \quad \operatorname{adj} A=\left[A_{i j}\right]_{2 \times 2}^T=\left[\begin{array}{cc}2 & 3 \\ -5 & -1\end{array}\right]^T=\left[\begin{array}{cc}2 & -5 \\ 3 & -1\end{array}\right]$

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