Matrices and Determinants
ID: #19 | Difficulty: easy
AI Quick Answer:
The correct option for this defence exam question is (A) which is -81. Detailed proof and explanation are supplied below.
If A is a square matrix of order 3 and its determinant |A| = -3, what is the value of the determinant |3A|?
Key Takeaways for NDA & CDS Candidates
- Ensure you recall the standard formulas for Matrices and Determinants during UPSC exam preparation.
- Eliminating obviously incorrect choices based on dimensional analysis or limits saves valuable seconds.
- Expert tip: Written defence mock tests should be practiced weekly with strict negative marking rules.
Correct Answer: (A)
-81
Step-by-Step Explanation
Using the properties of determinants, if A is a square matrix of order k, then the determinant of a scalar multiple of A, |cA|, is given by c^{k} \times |A|.
Here, the order k = 3, the determinant |A| = -3, and the scalar multiplier c = 3.
Thus, |3A| = 3^3 \times -3 = -81.
Here, the order k = 3, the determinant |A| = -3, and the scalar multiplier c = 3.
Thus, |3A| = 3^3 \times -3 = -81.
| Question Metadata Summary | |
|---|---|
| Exam Category | UPSC NDA / CDS / AFCAT / Agniveer |
| Subject Unit | NDA Maths Questions |
| Sub-topic / Module | Matrices and Determinants |
| Correct Option | Option (A) |
| Target Year | UPSC Defence Exams 2026 |