Singular Values & the SVD · Hard problem

Let $A = \begin{pmatrix}2 & 1 & 0\\1 & 2 & 0\\0 & 0 & -2\end{pmatrix}$. Find the minimum of $\|A - B\|_2$ (spectral norm) over all $3\times 3$ matrices $B$ of rank at most one.