If A is a square matrix of order 3 and $|A|= -2$ and , $|-2A^{-1}|$ is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4
{Solution}
We use the following determinant properties:
Here, \( A \) is of order 3 and \( |A| = -2 \), so:
\[
|-2A^{-1}| = (-2)^3 \cdot |A^{-1}| = -8 \cdot \frac{1}{|A|} = -8 \cdot \frac{1}{-2} = 4
\]