If A is a square matrix of order 4 and |adj A| = 8, then |A| =
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2
For a square matrix of order n, \( |\mathrm{adj}\,A|=|A|^{n-1} \). Here n = 4.
\( \displaystyle |A|^{3}=8 \)
\( \displaystyle |A|=2 \)
Why the other options are incorrect
Option (1) 5/2 — Incorrect. \( \left(\frac{5}{2}\right)^3=\frac{125}{8} \), not 8.
Option (2) \( 2\sqrt{2} \) — Incorrect. \( 2\sqrt{2} \) comes from \( |A|^2=8 \), that is, the formula for a matrix of order 3; for order 4 the power is 3.
Option (4) 64 — Incorrect. \( 64^3 \) is far larger than 8; 64 is \( 8^2 \), not a cube root of 8.