Question

Let \( A \) be a square matrix of order \(3\times3\). If \( |A|=-4 \), then the value of \[ \left|\frac{A^{-1}}{-2}\right| \] is:

• A. \(-1\)
• B. \(2\)
• C. \(\dfrac{1}{32}\)
• D. \(-\dfrac{1}{16}\)

Hint:

Remember: \[ |A^{-1}|=\frac1{|A|} \] and for an \(n\times n\) matrix, \[ |kA|=k^n|A| \] Always use the matrix order carefully while applying determinant properties.

Answer 1

The Correct Option is C