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Mathematics Question on Adjoint and Inverse of a Matrix

If A=[−26−5−1]A=\begin{bmatrix} -2&6\\\\-5&-1\end{bmatrix} then A−1A^{-1} is:

A

128[2−5\6−1]\frac{1}{28}\begin{bmatrix} 2&-5\\\6&-1\end{bmatrix}

B

132[−16−5−2]\frac{1}{32}\begin{bmatrix} -1&6\\\\-5&-2\end{bmatrix}

C

132[−1−6\5−2]\frac{1}{32}\begin{bmatrix} -1&-6\\\5&-2\end{bmatrix}

D

−128[−1−6−5−2]\frac{-1}{28}\begin{bmatrix} -1&-6\\\\-5&-2\end{bmatrix}

Answer

132[−1−6\5−2]\frac{1}{32}\begin{bmatrix} -1&-6\\\5&-2\end{bmatrix}

Explanation

Solution

The correct option is (C):132[−1−6\5−2]\frac{1}{32}\begin{bmatrix} -1&-6\\\5&-2\end{bmatrix}