Question

If \[S = \begin{bmatrix}a & b \\ c & d\end{bmatrix}\], then adj A is ____________ .

Options

• \[\begin{bmatrix}- d & - b \\ - c & a\end{bmatrix}\]

• \[\begin{bmatrix}d & - b \\ - c & a\end{bmatrix}\]

• \[\begin{bmatrix}d & b \\ c & a\end{bmatrix}\]

• \[\begin{bmatrix}d & c \\ b & a\end{bmatrix}\]

Answer 1

\[\begin{bmatrix}d & - b \\ - c & a\end{bmatrix}\]

Adjoint of a square matrix of order 2 is obtained by interchanging the diagonal elements and changing the signs of off-diagonal elements.

Here,

\[A = \begin{bmatrix} a & b\\c & d \end{bmatrix}\]

\[ \Rightarrow adj A = \begin{bmatrix} d & - b\\ - c & a \end{bmatrix}\]