Q54 / 155 · WBJEE 2025 · Mathematics
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$2^{n(n-1) / 2}$
- Correct answerD$3^{n(n-1) / 2}$
Solution
$3^{\frac{n(n-1)}{2}}$
Each diagonal entry must be ' 0 ' and sum of conjugate elements will be ' 0 '. So, we need to select elements of one side of the diagonal, where each entry has three options.
Hence, the correct answer is option: 'D'.