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.

Explanation

To prove that the matrix \( A \) defined by \( a_{ij} = \text{sgn}(i - j) \) is skew-symmetric, we will follow these steps:

### Step 1: Define the Matrix \( A \)

Given the definition of the elements of the matrix \( A \):
\[ a_{ij} = \text{sgn}(i - j) \]
...