If S = [ ll a & b c & d ], then adj A is - Vidyadip

MCQ

If $S =\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$, then $\operatorname{adj} A$ is

✓
$\left[\begin{array}{rr}d & -b \\ -c & a\end{array}\right]$
B
$\left[\begin{array}{ll}d & c \\ b & a\end{array}\right]$
C
$\left[\begin{array}{rr}-d & -b \\ -c & a\end{array}\right]$
D
$\left[\begin{array}{ll}d & b \\ c & a\end{array}\right]$

✓

Answer

Correct option: A.

$\left[\begin{array}{rr}d & -b \\ -c & a\end{array}\right]$

(a) $\left[\begin{array}{rr}d & -b \\ -c & a\end{array}\right]$
Explanation
$S =\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$
$\begin{array}{l} M _{11}= d \Rightarrow A _{11}= d \\ M _{12}= c \Rightarrow A _{12}=- c \\ M _{21}= b \Rightarrow A _{21}=- b \\ M _{22}= a \Rightarrow A _{22}= a \\ \Rightarrow \operatorname{Adj}( A )=\left[\begin{array}{rr}d & -b \\ -c & a\end{array}\right]\end{array}$

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