If A is a square matrix of order 2, then
Match List-I with List-II
| List-I | List-II | ||
| (A) | If \( |A|=3 \), then \( |2A|= \) | (I) | 16 |
| (B) | If \( |A|=2 \), then \( |3A|= \) | (II) | 12 |
| (C) | If \( |A|=1 \), then \( |4A|= \) | (III) | 64 |
| (D) | If \( |A|=4 \), then \( |4A|= \) | (IV) | 18 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) - (II), (B) - (IV), (C) - (I), (D) - (III)
For a square matrix of order 2, each of the two rows is multiplied by k:
\( \displaystyle |kA|=k^{2}|A| \)
(A) \( |2A|=2^{2}\times 3=12 \). This matches (II).
(B) \( |3A|=3^{2}\times 2=18 \). This matches (IV).
(C) \( |4A|=4^{2}\times 1=16 \). This matches (I).
(D) \( |4A|=4^{2}\times 4=64 \). This matches (III).
So the matching is (A) - (II), (B) - (IV), (C) - (I), (D) - (III).
CBSE Applied Mathematics (Class XII):
Properties of a Determinant
