Question

If \[ A= \begin{bmatrix} 2 & -3 & 1\\ -3 & 1 & -2\\ 1 & -2 & 3 \end{bmatrix}, \] then \(\operatorname{Adj}(A)=\)

• A. \[ \begin{bmatrix} 1 & -7 & 5\\ -7 & 5 & -1\\ 5 & -1 & 7 \end{bmatrix} \]
• B. \[ \begin{bmatrix} 1 & 7 & -5\\ 7 & 5 & 1\\ -5 & 1 & 7 \end{bmatrix} \]
• C. \[ \begin{bmatrix} -1 & 7 & 5\\ 7 & 5 & 1\\ 5 & 1 & -7 \end{bmatrix} \]
• D. \[ \begin{bmatrix} -1 & 7 & -5\\ 7 & -5 & 1\\ -5 & 1 & -7 \end{bmatrix} \]

Hint:

To find the adjoint of a \(3\times3\) matrix, first compute all nine cofactors carefully, paying attention to the signs \((+,-,+;\,-,+,-;\,+,-,+)\), and then take the transpose of the cofactor matrix.

Answer 1

The Correct Option is C