Matrices and Determinants
ID: #25 | Difficulty: easy
AI Quick Answer:
The correct option for this defence exam question is (A) which is -1280. Detailed proof and explanation are supplied below.
If A is a square matrix of order 4 and its determinant |A| = -5, what is the value of the determinant |4A|?
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)
-1280
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 = 4, the determinant |A| = -5, and the scalar multiplier c = 4.
Thus, |4A| = 4^4 \times -5 = -1280.
Here, the order k = 4, the determinant |A| = -5, and the scalar multiplier c = 4.
Thus, |4A| = 4^4 \times -5 = -1280.
| 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 |