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Mathematics Question on Matrices

If A is non-singular matrix and if A−1=12[−10−4\21]A^{-1}=\frac{1}{2}\begin{bmatrix} -10&-4\\\2&1\end{bmatrix}, then adj(A)=

A

[−1−4\210]\begin{bmatrix} -1&-4\\\2&10\end{bmatrix}

B

[104−2−1]\begin{bmatrix} 10&4\\\\-2&-1\end{bmatrix}

C

[14−2−10]\begin{bmatrix} 1&4\\\\-2&-10\end{bmatrix}

D

[−10−4\21]\begin{bmatrix} -10&-4\\\2&1\end{bmatrix}

E

[−1−4\102]\begin{bmatrix} -1&-4\\\10&2\end{bmatrix}

Answer

[104−2−1]\begin{bmatrix} 10&4\\\\-2&-1\end{bmatrix}

Explanation

Solution

The correct option is (B) : [104−2−1]\begin{bmatrix} 10&4\\\\-2&-1\end{bmatrix}