If A is square matrix of order 3 with |A| = 3, then |4 adj A| is equal to :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 576
Two standard results for a square matrix of order n are used:
\(|kB| = k^n|B|\)
\(|\mathrm{adj}\,A| = |A|^{n-1}\)
Here n = 3. Taking the scalar 4 out of the determinant:
\(|4\,\mathrm{adj}\,A| = 4^3\,|\mathrm{adj}\,A|\)
\(= 64\,|A|^{2}\)
\(= 64 \times 9\)
\(= 576\)