Question

If $A=\left[\begin{array}{cc}\alpha & \beta \\ \gamma & \alpha \end{array}\right]$, then Adj. A is equal to :

• A. $\left[\begin{array}{cc}\delta & -\gamma \\ -\beta & \alpha \end{array}\right]$
• B. $\left[\begin{array}{cc}\delta & -\beta \\ -\gamma & \alpha \end{array}\right]$
• C. $\left[\begin{array}{cc}-\delta & \beta \\ \gamma & -\alpha \end{array}\right]$
• D. $\left[\begin{array}{cc}-\delta & -\beta \\ \gamma & \alpha \end{array}\right]$

Answer 1

Answer: (B)

Let $A=\left[\begin{array}{cc}\alpha & \beta \\ \gamma & \delta \end{array}\right]$
$c_{11}=\delta ,c_{12}=-\gamma ,c_{21}=-\beta ,c_{22}=\alpha$
$\therefore \text{adj}A={\left[\begin{array}{cc}\delta & -\gamma \\ -\beta & \alpha \end{array}\right]}^{\prime }=\left[\begin{array}{cc}\delta & -\beta \\ -\gamma & \alpha \end{array}\right]$