Question

An \( n \times n \) matrix is formed using 0, 1 and -1 as its elements. The number of such matrices which are skew symmetric is:

• A. \( \frac{n(n-1)}{2} \)
• B. \( (n-1)^2 \)
• C. \( 2^{n(n-1)/2} \)
• D. \( 3^{n(n-1)/2} \)

Hint:

For skew symmetric matrices, set diagonal elements to 0 and use the condition \( a_{ij} = -a_{ji} \). Count the independent off-diagonal elements (\( \frac{n(n-1)}{2} \)) and compute the number of choices for each.