Question

If the matrix \(\begin{bmatrix}1 & 2\\ 3 & 4\end{bmatrix}\) has determinant \(k\), then the determinant of its adjoint is:

• A. \(k\)
• B. \(k^2\)
• C. \(1/k\)
• D. \(-k\)

Hint:

For 2×2 matrices, determinant of adjoint equals determinant.

Answer 1

The Correct Option is A

For an \(n\times n\) matrix, \[ \det(\text{adj }A) = (\det A)^{n-1} \] Here \(n=2\), so \(\det(\text{adj }A)=k\).