If A is a non-singular matrix of order 3 such that \(|\mathrm{adj}(A)| = 121\), then \(|AA^{T}|\) is equal to:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 121
For a square matrix of order n, \(|\mathrm{adj}(A)| = |A|^{n-1}\). Here n = 3:
\(|A|^2 = 121\)
By the product rule for determinants and \(|A^{T}| = |A|\):
\(|AA^{T}| = |A|\,|A^{T}| = |A|^2 = 121\)
The value of \(|A|\) itself (11 or −11) is not needed, because only \(|A|^2\) appears.