Question

An `nxxn` matrix is formed using 0,1 and -1 as its elements. The number of such matrices which are skew-symmetric, is
A. `(n(n+1))/2`
B. `(n-1)^2`
C. `2^((n(n-1))/(2))`
D. `3^((n(n-1))/(2))`

Answer 1

Correct Answer - D
All leading diagonal elements of a skew-symmetric are zero. So, to form a skew-symmketric matrix `A=[a_(ij)]` of orden `nxxn`, we need to know the elements `a_(ij)" for " iltj,I,j=1,2,…,n`, Each one of these `(n^2-n)/2`elements can take three values 0,1, and -1. So, the number of skew-symmetric matrices is `3^((n^2-n)/2)`=3^((n(n-1))/2)`