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. If A and B are square matrices of order 3 such that |A| = –1, |B| = 3, then |3AB| is equal to
- a)–9
- b)–81
- c)–27
- d)81
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
. If A and B are square matrices of order 3 suchthat |A| = –1, |...
Since the determinant of a matrix is a scalar quantity, we can write:
|A| = k|B|
where k is some constant. We are given that |A| = 2 and |B| = 3, so we can substitute these values:
2 = k(3)
Solving for k, we get:
k = 2/3
Now, we can use the fact that the determinant of a product of matrices is equal to the product of the determinants:
|AB| = |A||B|
Substituting the given determinants and the value of k, we get:
|AB| = 2/3 * 3
|AB| = 2
Therefore, the determinant of the product AB is 2.
|A| = k|B|
where k is some constant. We are given that |A| = 2 and |B| = 3, so we can substitute these values:
2 = k(3)
Solving for k, we get:
k = 2/3
Now, we can use the fact that the determinant of a product of matrices is equal to the product of the determinants:
|AB| = |A||B|
Substituting the given determinants and the value of k, we get:
|AB| = 2/3 * 3
|AB| = 2
Therefore, the determinant of the product AB is 2.
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. If A and B are square matrices of order 3 suchthat |A| = –1, |...
|3AB| = |3A| × |B|
→|3A| = 27 × |A| = 27×-1 = -27
Thus, |3AB| = -27×3 = -81
Hence, option 'B' is correct.
→|3A| = 27 × |A| = 27×-1 = -27
Thus, |3AB| = -27×3 = -81
Hence, option 'B' is correct.
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. If A and B are square matrices of order 3 suchthat |A| = –1, |B| = 3, then |3AB| is equal toa)–9b)–81c)–27d)81Correct answer is option 'B'. Can you explain this answer?
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