Determinants
If A and B are square matrices of order 3 such that |A| = 2 and |B| = 3, then |AB| equals
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Solution
6
- Determinant of Product: A fundamental property of determinants states that for any two square matrices A and B, ∣AB∣=∣A∣×∣B∣.
- Application:
- ∣AB∣=(2)×(3)=6.
- Result: The determinant of the product is 6. Note that this property holds regardless of the matrix size of order n.
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About This Question
- Subject
- mathematics
- Chapter
- matrices and determinants
- Topic
- determinants
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
6
- Determinant of Product: A fundamental property of determinants states that for any two square matrices A and B, ∣AB∣=∣A∣×∣B∣.
- Application:
- ∣AB∣=(2)×(3)=6.
- Result: The determinant of the product is 6. Note that this property holds regardless of the matrix size of order n.
This easy difficulty mathematics question is from the chapter matrices and determinants, covering the topic of determinants. It appeared in the 2025 exam.
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