Question

If $A = \begin{bmatrix}\alpha&\beta\\ \gamma&\alpha\end{bmatrix}$, then Adj. A is equal to :

• A. $\begin{bmatrix}\delta & - \gamma\\ - \beta & \alpha\end{bmatrix}$
• B. $\begin{bmatrix}\delta & - \beta \\ - \gamma & \alpha\end{bmatrix}$
• C. $\begin{bmatrix} - \delta & \beta \\ \gamma & - \alpha\end{bmatrix}$
• D. $\begin{bmatrix} - \delta & - \beta \\ \gamma & \alpha\end{bmatrix}$

Answer 1

Answer: (B)

Let $A = \begin{bmatrix} \alpha & \beta \\ \gamma & \delta \end{bmatrix}$
$c_{11} = \delta , c_{12} = -\gamma, c_{21} = - \beta, c_{22} = \alpha$
$ \therefore \text{adj}A = \begin{bmatrix}\delta&-\gamma\\ -\beta&\alpha\end{bmatrix}' = \begin{bmatrix}\delta&-\beta\\ -\gamma&\alpha\end{bmatrix}$