Question

If a square matix a of order three is defined `A=[a_("ij")]` where `a_("ij")=s g n(i-j)`, then prove that A is skew-symmetric matrix.

Answer 1

We know that
`sgn(x)={("1, if "x gt 0),(-"1, if "xlt0),("0, if "x=0):}`
`:. a_("ij")=sgn (i-j)={("1, if "igt j),(-"1, if "i ltj),("0, if "i=j):}`.
`:. A=[(0,-1,-1),(1,0,-1),(1,1,0)]`
Hence, matrix A is skew-symmetric.