If \( A \) is a diagonal matrix of order 3 with diagonal elements as 2, 3, 4, then |adj A| is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 576
The determinant of a diagonal matrix is the product of its diagonal elements:
\( \displaystyle |A|=2\times 3\times 4=24 \)
For a square matrix of order n, \( |\mathrm{adj}\,A|=|A|^{n-1} \). Here n = 3:
\( \displaystyle |\mathrm{adj}\,A|=|A|^{2} \)
\( \displaystyle =24^2=576 \)
Why the other options are incorrect
Option (1) 24 — Incorrect. 24 is |A| itself, not |adj A|.
Option (2) 288 — Incorrect. The value is \( 24^2=576 \), not 288.
Option (4) 13824 — Incorrect. 13824 is \( 24^3=|A|^{n} \); the power is n − 1 = 2, not n = 3.