If \(A\) is a square matrix of order 3 and \(|A|= 5\), then the value of \(|-AA^T|\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(-25\)
For a matrix of order n, \(|kA| = k^n|A|\). Here \(-AA^T = (-1)(AA^T)\) and n = 3:
\(|-AA^T| = (-1)^3\,|AA^T|\)
By the product rule for determinants, and since \(|A^T| = |A|\):
\(|AA^T| = |A|\,|A^T| = 5 \times 5 = 25\)
So
\(|-AA^T| = -25\)