Chapter 2 - Matrices - 2.2 Properties of Matrix Operations - 2.2 Exercises - Page 61: 70

Since $$A^T=\left[\begin{array}{ccc}{0}&{-2} &{1} \\{2}&{0}& {3}\\{-1}&{-3}&{0} \end{array}\right] =-A,$$ then $A$ is skew-symmetric.

Let the matrix $A$ be given by $$A=\left[\begin{array}{ccc}{0}&{2} &{-1} \\{-2}&{0}& {-3}\\{1}&{3}&{0} \end{array}\right].$$ Since $$A^T=\left[\begin{array}{ccc}{0}&{-2} &{1} \\{2}&{0}& {3}\\{-1}&{-3}&{0} \end{array}\right] =-A,$$ then $A$ is skew-symmetric.