Orthogonality & Least Squares · Superchallenge problem

Give the space of real $3\times 3$ matrices the Frobenius inner product $\langle X, Y\rangle = \operatorname{tr}(X^{T}Y)$ (the sum of products of corresponding entries). Let $W$ be the subspace of symmetric matrices with trace $0$. Find the distance from $A = \begin{pmatrix}1 & 2 & 3\\4 & 5 & 6\\7 & 8 & 9\end{pmatrix}$ to $W$.