= Solution
\b[Yes.] Part (a) diagonalizes $G=B$, whose <spectral radius> is $3/8<1$. Thus
$$
G^n=S\operatorname{diag}(0^n,(3/8)^n)S^{-1}\longrightarrow0\qquad(n\geq1),
$$
and every initial error converges to zero. For the specified initial vector, solving $Ax=b$ gives $x=(1,-1)^T$ and $e_0=(-1,1)^T$. In fact,
$$
\boxed{e_n=(3/8)^n\begin{pmatrix}-2\\1\end{pmatrix},\quad
x_n=\begin{pmatrix}1-2(3/8)^n\\-1+(3/8)^n\end{pmatrix}\quad(n\geq1).}
$$
The special formula is not asserted for $n=0$, because the zero-eigenvalue component disappears only after the first step.
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