Solution
= Solution
On the same <basis>, $Y=D^2$ kills $v,u$ and sends $w$ to $16w$. Explicitly,
$$
D^2=\begin{pmatrix}7&4&5\\7&4&5\\7&4&5\end{pmatrix}.
$$
Thus all three <basis> lines are <submodules> after <restriction of scalars>, and
$$
\boxed{{}_BM\cong B/(Y)\oplus B/(Y)\oplus B/(Y-16).}
$$
Each summand is a <simple module>, hence an <indecomposable module>. Squaring has destroyed the length-two <nilpotent> <Jordan chain>.