Let \(W\) be a subspace of \(\mathbb{R}^{2\times 2}\) having an ordered basis given by \(\Gamma = \left( \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}, \begin{bmatrix} 0 & 2 \\ 2 & 0 \end{bmatrix} \right).\) Let \(u = \begin{bmatrix} 3 & -2 \\ -2 & 3\end{bmatrix}\). Then \([u]_\Gamma = \begin{bmatrix} a \\ -1\end{bmatrix}\).
What is \(a\)?