If \(A = \begin{bmatrix}6&k\\-4&-6\end{bmatrix}\) and \(A^2 = O\), where O is the zero matrix of order 2, then the value of k is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 9
Multiplying A by itself, row by column:
\( \displaystyle A^2 = \begin{bmatrix}36 - 4k&6k - 6k\\-24 + 24&-4k + 36\end{bmatrix} = \begin{bmatrix}36 - 4k&0\\0&36 - 4k\end{bmatrix} \)
\(A^2 = O\) gives
\(36 - 4k = 0\)
\(k = 9\)