Matrix Properties
If A is a skew-symmetric matrix of odd order, then |A| equals
Select the correct option:
🔒 Solution Hidden from View
Submit your answer to unlock the detailed step-by-step solution.
More matrices and determinants Practice Questions
If A and B are symmetric matrices of the same order, then AB is symmetric if
If A and B are symmetric matrices of the same order, then AB is symmetric if
The trace of a square matrix A is defined as the sum of its diagonal elements. If A = [[1, 2, 3], [4...
The trace of a square matrix A is defined as the sum of its diagonal elements. If A = [[1, 2, 3], [4...
The area of the triangle with vertices at the points (1, 2), (4, 6) and (7, 2) in the coordinate pla...
The area of the triangle with vertices at the points (1, 2), (4, 6) and (7, 2) in the coordinate pla...
Let A be the two by two matrix with rows (2, 1) and (1, 2); using the Cayley-Hamilton theorem, the m...
Let A be the two by two matrix with rows (2, 1) and (1, 2); using the Cayley-Hamilton theorem, the m...
For any skew-symmetric matrix of odd order, the determinant always takes a fixed value; the determin...
For any skew-symmetric matrix of odd order, the determinant always takes a fixed value; the determin...
The homogeneous system of equations with coefficient matrix rows (1, 2, 3), (2, k, 6) and (1, 1, 1) ...
The homogeneous system of equations with coefficient matrix rows (1, 2, 3), (2, k, 6) and (1, 1, 1) ...
The value of the real parameter k for which the matrix with rows (k, 2, 3), (2, k, 1) and (3, 1, k) ...
The value of the real parameter k for which the matrix with rows (k, 2, 3), (2, k, 1) and (3, 1, k) ...
If A and B are square matrices of order 3 with det(A) = 3 and det(B) = -2, then the determinant of t...
If A and B are square matrices of order 3 with det(A) = 3 and det(B) = -2, then the determinant of t...
A square matrix A is called idempotent when it satisfies A squared equal to A; for such a matrix the...
A square matrix A is called idempotent when it satisfies A squared equal to A; for such a matrix the...
If A is a square matrix of order 2 with trace equal to 5 and determinant equal to 6, then the sum of...
If A is a square matrix of order 2 with trace equal to 5 and determinant equal to 6, then the sum of...
A square matrix A is nilpotent if some positive integer power of A equals the zero matrix; the deter...
A square matrix A is nilpotent if some positive integer power of A equals the zero matrix; the deter...
Applying the property that adding a multiple of one row to another leaves a determinant unchanged, t...
Applying the property that adding a multiple of one row to another leaves a determinant unchanged, t...
About This Question
- Subject
- mathematics
- Chapter
- matrices and determinants
- Topic
- matrix properties
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
0
- Definition: For a skew-symmetric matrix A, AT=−A.
- Apply Determinant: ∣AT∣=∣−A∣.
- Properties:
- ∣AT∣=∣A∣
- ∣−A∣=(−1)n∣A∣, where n is the order.
- Constraint of Odd Order: If n is odd, (−1)n=−1.
- Thus, ∣A∣=−∣A∣⟹2∣A∣=0⟹∣A∣=0.
- Result: The determinant of an odd-order skew-symmetric matrix is always zero.
This hard difficulty mathematics question is from the chapter matrices and determinants, covering the topic of matrix properties. It appeared in the 2025 exam.
Looking for more practice? Explore all mathematics questions or browse matrices and determinants questions on RankGuru.