Question

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

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

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

(c) $\left[\begin{array}{cc}d& b\\ c& a\end{array}\right]$

(d) $\left[\begin{array}{cc}d& c\\ b& a\end{array}\right]$

Answer 1

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

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

Here,

$$\begin{gathered} A=\left[ab \\ cd\right] \\ \Rightarrow adjA=\left[d-b \\ -ca\right] \end{gathered}$$