Matrices and Determinants
Properties of Determinants
Premium Question
Grade 12
Question:
If $A$ is a skew-symmetric matrix of odd order $n$, then $|A|$ equals:
(1) $0$
(2) $1$
(3) $-1$
(4) $n$
Step-by-Step Solution
Key Concept: Use $A^T = -A$ together with $|A^T| = |A|$ and $|kA| = k^n|A|$ to obtain an equation of the form $|A| = (-1)^n|A|$, and see what this forces when $n$ is odd.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)