Solution
= Solution
Subtract the first row from the third. Expansion along the resulting row $(a-1,0,0)$ gives the <determinant>
$$
\det A=(a-1)\det\begin{pmatrix}2&3\\1&a-1\end{pmatrix}
=\boxed{(a-1)(2a-5)}.
$$
Hence
$$
\boxed{\det A=0\iff a=1\text{ or }a=\frac52}.
$$