Question

If for a matrix \( A \), \( |A| = 6 \) and \[ \operatorname{adj}A = \begin{bmatrix} 1 & -2 & 4
4 & 1 & 1
-1 & k & 0 \end{bmatrix}, \] then \( k \) is equal to:

• A. \( -1 \)
• B. \( 1 \)
• C. \( 2 \)
• D. \( 0 \)

Hint:

Key identities: \begin{itemize} \item \( |\operatorname{adj}A| = |A|^{n-1} \) \item Useful for finding unknown entries. \end{itemize}

Answer 1

The Correct Option is D