If I is the identity matrix of order 3 and \(|kI| = -8\), then the value of k is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(-2\)
The matrix kI is the scalar matrix with k in each of the 3 diagonal places and 0 elsewhere:
\( \displaystyle kI = \begin{bmatrix} k & 0 & 0 \\ 0 & k & 0 \\ 0 & 0 & k \end{bmatrix} \)
Its determinant is the product of the diagonal elements:
\(|kI| = k^3\)
\(k^3 = -8\)
\(k = -2\)
A cube keeps the sign, so \(k = 2\) would give \(+8\); only the real value \(-2\) works.