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