Matrix Properties

Question

If A is a skew-symmetric matrix of odd order, then |A| equals

RankGuru · Accepted Answer

1. **Definition**: For a skew-symmetric matrix $A$, $A^T = -A$.
2. **Apply Determinant**: $|A^T| = |-A|$.
3. **Properties**:
   - $|A^T| = |A|$
   - $|-A| = (-1)^n |A|$, where $n$ is the order.
4. **Constraint of Odd Order**: If $n$ is odd, $(-1)^n = -1$.
   - Thus, $|A| = -|A| \implies 2|A| = 0 \implies |A| = 0$.
5. **Result**: The determinant of an odd-order skew-symmetric matrix is always zero.

Rank Guru

Matrix Properties

Select the correct option:

Solution

🔒 Solution Hidden from View

More matrix properties Practice Questions

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...

About This Question