If A is an invertible matrix of order 3 and \( |A|=7 \), then the value of \( |\mathrm{adj}\,A| \) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 49
For a square matrix A of order n, \( |\mathrm{adj}\,A|=|A|^{\,n-1} \). Here \( n=3 \) and \( |A|=7 \):
\( \displaystyle |\mathrm{adj}\,A|=7^{3-1} \)
\( \displaystyle =7^{2}=49 \)
Why the other options are incorrect
Option (1) 14 — Incorrect. 14 = 2 × 7; |A| must be raised to the power n − 1 = 2, not multiplied by 2.
Option (2) 343 — Incorrect. 343 = \( 7^{3} \) uses the power n = 3 instead of n − 1 = 2.
Option (4) 7 — Incorrect. 7 is |A| itself; \( |\mathrm{adj}\,A|=|A| \) only for a 2 × 2 matrix.
CBSE Applied Mathematics (Class XII):
Adjoint of a Matrix
