1.4.18 Matrix transformations

condition: For the matrix \( L=\left(\begin{array}{ccc}2 & 1 & 2 \\ 0 & 0 & -1 \\ 4 & -1 & 1\end{array}\right) \) check: a) whether the matrix \( \frac{1}{2}\left(L-L^{T}\right) \) skew-symmetric; b) is the equality \( L^{2}=3 \cdot L \) true?