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Question
If \[S = \begin{bmatrix}a & b \\ c & d\end{bmatrix}\], then adj A is ____________ .
Options
\[\begin{bmatrix}- d & - b \\ - c & a\end{bmatrix}\]
\[\begin{bmatrix}d & - b \\ - c & a\end{bmatrix}\]
\[\begin{bmatrix}d & b \\ c & a\end{bmatrix}\]
\[\begin{bmatrix}d & c \\ b & a\end{bmatrix}\]
Solution
\[\begin{bmatrix}d & - b \\ - c & a\end{bmatrix}\]
Adjoint of a square matrix of order 2 is obtained by interchanging the diagonal elements and changing the signs of off-diagonal elements.
Here,
\[A = \begin{bmatrix} a & b\\c & d \end{bmatrix}\]
\[ \Rightarrow adj A = \begin{bmatrix} d & - b\\ - c & a \end{bmatrix}\]
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