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Mathematics Question on Determinants

If A=[−26 −57]A = \begin{bmatrix}-2&6\\\ -5&7\end{bmatrix} , then adj A:

A

[7\-6 5\-2] \begin{bmatrix} 7 & \- 6 \\\ 5 & \- 2 \end{bmatrix}

B

[2\-6 5\-7] \begin{bmatrix} 2 & \- 6 \\\ 5 & \- 7 \end{bmatrix}

C

[7\-5 6\-2] \begin{bmatrix} 7 & \- 5 \\\ 6 & \- 2 \end{bmatrix}

D

None of the above

Answer

[7\-6 5\-2] \begin{bmatrix} 7 & \- 6 \\\ 5 & \- 2 \end{bmatrix}

Explanation

Solution

We know for any matrix A=[ab cd]A= \begin{bmatrix}a&b\\\ c&d\end{bmatrix} adj(A)=[d−b −ca]\text{adj} \left(A\right) = \begin{bmatrix}d&-b\\\ -c&a\end{bmatrix} If A=[−26 −57]⇒adjA=[7−6 5−2]A = \begin{bmatrix}-2&6\\\ -5&7\end{bmatrix} \Rightarrow \text{adj}A= \begin{bmatrix}7&-6\\\ 5&-2\end{bmatrix}