If A is a square matrix of order 3 and |adj A| = 3, then |A| is equal to :
(A) \( \sqrt{3} \)
(B) \( -\sqrt{3} \)
(C) 9
(D) \( -9 \)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) and (B) only
For a matrix of order 3, \( |\mathrm{adj}\,A|=|A|^{2} \), so
\( |A|^{2}=3 \)
A determinant can be negative, so both square roots are possible.
So \( |A|=\sqrt{3} \) or \( |A|=-\sqrt{3} \).
Checking the statements
(A) \( \sqrt{3} \) — Correct. \( (\sqrt{3})^{2}=3 \).
(B) \( -\sqrt{3} \) — Correct. \( (-\sqrt{3})^{2}=3 \).
(C) 9 — Incorrect. \( 9^{2}=81 \), not 3.
(D) \( -9 \) — Incorrect. \( (-9)^{2}=81 \), not 3.